𝕿𝖊𝖈𝖍𝖗𝖎𝖌𝖍𝖙𝖘 Bulletin for Friday, January 07, 2022 ┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅ Generated Sat 8 Jan 02:40:53 GMT 2022 Created by Dr. Roy Schestowitz (𝚛𝚘𝚢 (at) 𝚜𝚌𝚑𝚎𝚜𝚝𝚘𝚠𝚒𝚝𝚣 (dot) 𝚌𝚘𝚖) Full hyperlinks for navigation omitted but are fully available in the originals The corresponding HTML versions are at 𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈 Latest in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕 and older bulletins can be found at 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒕𝒙𝒕-𝒂𝒓𝒄𝒉𝒊𝒗𝒆𝒔 Full IPFS index in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔 and as plain text in 𝒉𝒕𝒕𝒑://𝒕𝒆𝒄𝒉𝒓𝒊𝒈𝒉𝒕𝒔.𝒐𝒓𝒈/𝒊𝒑𝒇𝒔/𝒕𝒙𝒕 Gemini index for the day: gemini://gemini.techrights.org/2022/01/07/ ╒═══════════════════ 𝐑𝐄𝐂𝐄𝐍𝐓 𝐁𝐔𝐋𝐋𝐄𝐓𝐈𝐍𝐒 ════════════════════════════════════╕ Previous bulletins in IPFS (past 21 days, in chronological order): QmRKnWzns1EsWaoxUGG5KEEhiyhSELGYVdfVqSB5Ay4qhc QmZdVw5kGwFeXoGNexLWZDS8MJxeGKAeup4JpiAnmE946y QmYdAKSfCu9puR3SWGWwGW19Uzo1jj4L1aYpeGqpC5FCp6 QmZP4LnsTHrznHVdokybFZafDLWJqRPKyvvberG4dVRasQ QmfL4kPLDVa6CGiB1yXozobGCQ5fTPahv8T7hPstsxvkie QmP2Y5UBBDqcCEECSknvoPU6WVjL4V93dQMbKj34jYv56N QmTTqHT1gu1SWzp4ejhsMMHeEr1cnaDHeAQnawx8obkmR5 QmVjqVfy1bLLkjPbYtUagNsq6vfXCToNocEPu1s2Cvo3ab QmXVB3t7bvESJpBXVnHEH2koE5NY8MqsHXWVco5dbnNW1M QmUnmYrNuwB9WxrYeqcbFyf8Bew66hMkdU1YVc9WsKh4JC QmYjUQnBiQsqQMypkyvfTj7b9arksYuzUe1BzJ9a6JUTk4 QmarLrYBMcbMFgab1qAkPGRjRr57niwUpd5PEPbMp8225S QmYYUiUwcwdiuMNs9EXu5Ci3ELNhZcY4b7JsFUZqp7drnc QmTWhb5PucmgsMLVAJufczuFnxY37RcgjXGMTczMdhndPd QmVgY18p35Thp6aWh7cRUuoocqLYGYFW2QnLEJhuqn69Kw QmcN2LseMFZtt5HtSJMT5h9HDZa4ZNy6B7uWe7gK8fPeF9 QmfH2by4K6HCiZyvyGQ1L5syH6ZSfcHH12ph6TDo82aovk QmbfkzNgEcSLWg1uktyXVKRqXdn8cURLS2BGZZ8j7BRu53 QmYyjvuyCsmKepqGvikeVazrauZqV2sNgUg5p2UhdxvGXe QmeizGYhw45pUpaYcuwBfE8NWgRhpFbkNtg8fZ7tGbAMXw QmfKHqGowjRxdQqskGCLaTJvfCGFi19QHkyd8kwa9PMJ21 ╒═══════════════════ 𝐈𝐍𝐃𝐄𝐗 ═══════════════════════════════════════════════════╕ ⦿ [Meme] Just Another Battistelli | Techrights ⦿ The EPO’s Race to the Bottom — Part V — An Assault on Pensioners | Techrights ⦿ Fictional Gaps and an Attack on Workers | Techrights ⦿ IRC Proceedings: Thursday, January 06, 2022 | Techrights ⦿ Techrights Updates: Metadata in Videos and More | Techrights ⦿ [Meme] Diferençampinos | Techrights ䷼ Bulletin articles (as HTML) to comment on (requires login): http://techrights.org/2022/01/07/another-battistelli/#comments http://techrights.org/2022/01/07/epo-going-after-pensioners/#comments http://techrights.org/2022/01/07/fictional-epo-gap/#comments http://techrights.org/2022/01/07/irc-log-060122/#comments http://techrights.org/2022/01/07/techrights-videos-metadata/#comments http://techrights.org/2022/01/07/the-gap/#comments ䷞ Followed by Daily Links (assorted news picks curated and categorised): http://techrights.org/2022/01/07/chimeraos-29/#comments http://techrights.org/2022/01/07/kdenlive-21-12-1/#comments ䷩ 𝚕𝚒𝚗𝚎 63 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/07/another-battistelli/#comments Gemini version at gemini://gemini.techrights.org/2022/01/07/another-battistelli/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Just_Another_Battistelli⠀✐ Posted in Europe, Patents at 12:22 pm by Dr. Roy Schestowitz 5 years ago: Judge_Cuno_Tarfusser_Wants_to_Become_the_Next_EPO_President 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇3 years, António, EPO still failing⦈ Summary: Tomorrow (or today) António_Campinos celebrates 3.5 years as EPO President; based on internal documents, he has done nothing concrete to save the EPO from corrupt management (in some ways he has deepened the crisis) ⠀⠀⠀⠙⠋⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣤⣿⣷⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠹⡏⣿⡍⣩⣭⣩⣭⣝⡛⣛⣛⡻⢿⠿⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠛⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠉⣽⣾⣟⢠⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⡇⣿⣿⠈⡟⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⣀⣤⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠛⠻⠟⢃⣴⣥⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠁⠐⣿⣿⣿⢿⣷⣶⣿⣷⣤⣤⣤⣭⣵⣭⣭⣼⣿⣟⣛⣃⣻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣧⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠸ ⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣫⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀ ⠀⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶ ⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢐⠒⠂⠀⠀⠀⠀⠀⡘⠻⠿⠇⠀⠀⢀⣀⣤⣾⣿⣿ ⠀⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠈⠙⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣤⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⣀⣠⣴⡾⠿⠛⠃⠉⠓⠀⢸⡿⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠛⠋⠙⠟⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⡿⢟⣷⠶⠿⠛⠉⠁⠀⠀⠀⠀⢆⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿ ⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⠙⡿⠀⠀ ⣿⣆⠀⠀⠀⢠⣄⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁ ⣿⣿⣆⠀⠀⣿⣿⣧⣰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⢸⡿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⣿⣿⣿⡇⠀⢸⡏⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠸⠁⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀ ⢿⣿⣿⣧⠀⠰⠀⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇⠠⣾ ⠀⢿⣿⣿⠀⢸⡅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⢱⣄⣿ ⣀⣈⣿⣿⠀⢸⣏⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⢸⣿⠜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠐⠒⠒⠒⠒⢒⣒⣒⣲⣶⣶⣶⣾⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣈ ⠀⠀⠀⠙⠋⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣥⣭⣯⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠹⡏⣿⡍⣩⣭⣩⣭⣍⡛⣛⣛⡻⢿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠛⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠉⣽⣾⣟⢀⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⡇⣿⣿⠘⡿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⣀⣤⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠛⠻⠟⢃⣤⣅⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠁⠐⣾⣿⣿⣿⣿⣷⣿⣷⣤⣤⣤⣭⣵⣭⣭⣽⣿⣟⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⡉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⢘⣛⣧⡆⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠸ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡿⢛⠁⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠸ ⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀ ⠀⠹⣿⣿⣿⣿⣇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾ ⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⠛⠉⠀⠀⠀⠀⠀⢀⣉⣛⣃⣀⣠⣠⣤⣴⣾⣿⣿ ⠀⠀⠀⠹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠈⠻⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⣀⣠⣴⡾⠿⠟⠃⠉⠃⠀⠸⠿⢦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠛⠉⠙⠋⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⡿⢟⣷⠶⠿⠛⠉⠁⠀⠀⠀⠀⢆⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠿⠿⠿⠿⠛⢿⣿⣿⠿⠛ ⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡿⡀⠀ ⣿⣆⠀⠀⠀⢠⣄⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑ ⣿⣿⣆⠀⠀⢿⣿⣶⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠂⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡆⠀⢸⡿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⠿⠟⠛⠙⠃⠀⠀⠸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤ ⣿⣿⣿⡇⠀⢸⡏⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠈⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀ ⢿⣿⣿⣧⠀⠰⠀⠽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇⠠⣾ ⠈⢻⣿⣿⠀⢸⡅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡑⢱⣄⣿ ⣀⣈⣿⣿⠀⢸⣏⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⢸⣿⠜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠒⠒⠒⠒⢒⣒⣒⣲⣶⣶⣶⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣈ ⠀⠀⠀⠙⠋⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣬⣭⣥⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠸⡟⣷⡍⣩⣭⣩⣭⣝⡛⣛⣛⡻⢿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠛⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠉⣽⣾⣟⢰⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⡇⣿⣿⠸⡷⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⣀⣤⡀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠛⠻⠟⢃⣸⡇⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⣀⣠⣴⡾⠿⠟⠋⠉⠀⠀⢠⡶⢆⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⡿⢛⣷⠶⠿⠋⠉⠁⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠉⣡⣶⡀⠀⠰ ⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⡿⣀⠐ ⣿⣆⠀⠀⠀⢠⣄⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱ ⣿⣿⣆⠀⠀⣿⣿⣵⣰⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⢸⡿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤ ⣿⣿⣿⡇⠀⢸⡇⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠈⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀ ⢿⣿⣿⣧⠀⠰⠀⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠠⣾ ⠀⢻⣿⣿⠀⢰⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡑⢱⣄⣿ ⣀⡈⣿⣿⠀⢸⣟⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⢸⣿⠘ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠠⣤⣿⣷⡦⣴⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠒⠒⠒⠒⢒⣒⣒⣲⣿⣿⣿⣽⣷⣶⣤⣀⣠⣀⣀⣈ ⠀⠀⠀⠙⠋⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⢸⡏⣶⡌⣩⣭⣩⣭⣍⡛⣛⣛⡿⢿⠷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠛⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠉⣽⣾⣟⠰⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⣿⡇⣿⣿⢸⣿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢺⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⣠⣤⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠛⠻⠟⠃⠸⠅⠸⢿⢇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠀⠈⣿⠀⠀⠀⠀⠞⠀⢸⣿⣿⣿⣾⣶⣾⣿⣷⣤⣤⣤⣭⣵⣭⣭⣽⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣇⠀⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⡻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠸ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⠀⢀⠀⠀⠸ ⠻⣿⣿⣿⣿⣧⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠ ⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣙⠛⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿ ⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⢀⣀⣤⣶⡾⠿⠛⠁⠉⠀⠀⢀⠶⠉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠟⢿⡿⠿⠿⠿⢿ ⠀⠀⠀⠀⠀⢻⡿⢟⣷⠶⠟⠋⠉⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⣠⣴⡄⠀⠘ ⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠿⣀⡘ ⣿⣆⠀⠀⠀⢠⣄⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣟⣽⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱ ⣿⣿⣆⠀⠀⣿⣿⣷⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡆⠀⢸⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⢸⡏⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠀⠨⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀ ⢿⣿⣿⣧⠀⠰⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢠⣾ ⠀⢻⣿⣿⠀⢸⣄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡃⢳⣄⣿ ⣀⣈⣿⣿⠀⢸⣋⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⢸⣿⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⣀⣠⣶⣂⣀⣠⣄⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⡀⣀⠀⠀⠀⠀⠒⠒⠒⠒⢒⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⣈ ⠀⠀⠀⠛⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⢸⡏⣷⡌⣩⣥⣨⣭⣝⡛⣛⣛⡿⢷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠃⠀⠀⢀⣶⡆⠀⠀⠀⠀⠀⠉⣽⣾⣟⢸⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⣿⡇⣿⣿⠀⣿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻ ⢀⣠⣤⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠛⠻⠟⠃⣸⡇⠸⢿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⠀⠀⠀⠘⣿⠀⠀⠀⢀⠎⠘⠲⣷⣷⣶⣾⣶⣾⣿⣷⣤⣤⣤⣭⣵⣭⣭⣽⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣇⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠹⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠠ ⢻⣿⣿⣿⣿⣇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣂⠀⣄⣠⣄⠀⠀⠀⠉⠀⠰⣶ ⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⢀⣿⣦⣠⣶⣾⣿⣿⣿⣿⣶⣄⣤⣤⣶⣾⣿ ⠀⠀⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⢀⣠⣤⣶⠿⠟⠛⠁⠀⠀⠀⠀⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠙⠿⠛⢛⡛⣛ ⠀⠀⠀⠀⠈⣿⡿⣿⡶⠾⠛⠉⠉⠀⠀⠀⠀⠀⢄⢀⣀⣴⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣴⣦⡀⠁⠹ ⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⢀⣠⡄⠀⠀⠛⠛⢧⣀⢸ ⣿⡄⠀⠀⠀⣤⣄⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡞⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⢹⣟⠃⠀⠀⠀⠀⠐⠛⢠ ⣿⣿⣄⠀⠀⣿⣿⣆⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⣿⣿⣿⠀⠀⢿⢹⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⠀⠘⢸⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⢀ ⣿⣿⣿⡇⠀⠔⠈⠙⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢰⣿ ⠘⣿⣿⣧⠀⢸⣭⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠉⣦⣘⣿ ⣀⣘⣿⣿⠀⣸⣛⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⣿⣷⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣒⣒⣖⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣴⣦⣤⣄⣀⣀⣠ ⠀⠀⠀⠛⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⢹⡏⣷⡌⣩⣥⣩⣭⣝⡛⣛⣛⡻⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠃⠀⠀⢠⣾⡀⠀⠀⠀⠀⠀⠉⣽⣾⣟⢸⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡇⣿⣿⢀⣿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠓ ⢀⣤⣤⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠛⠻⠟⠃⣼⡗⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣇⠀⠀⠀⠸⣷⠀⠀⠀⢀⠎⠘⠺⣿⣿⣿⣽⣷⣾⣿⣷⣤⣤⣤⣭⣵⣭⣭⣽⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡄⠀⠀⠀⢹⡇⠀⠀⠈⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⢠ ⣿⣿⣿⣿⣿⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠄ ⢿⣿⣿⣿⣿⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢠⣬ ⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠠⣙⣧⣀⣀⣀⣀⣤⣤⣤⣤⣾⣿ ⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⣀⣠⣴⣶⠿⠛⠛⠁⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠙⠉⠙⠛⠛⠻⠛⣻ ⠀⠀⠀⠀⠘⣿⠟⣯⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⢦⢀⣀⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣴⣤⡀⠃⢹ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉⠹⢧⣀⢸ ⣿⡄⠀⠀⠀⣴⣄⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⡞⣻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠁⠀⠀⠀⠀⠘⠉⢀ ⣿⣿⡄⠀⠀⣿⡿⣆⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⠀⠀⣿⣷⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⣿⣿⣿⠀⠀⢿⢹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡦⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡀⠀⠸⢸⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⢀ ⣿⣿⣿⡇⠀⠒⠈⠛⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢰⣿ ⠙⣿⣿⡇⠀⢸⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣦⣼⣿ ⣀⣹⣿⣇⠀⣸⣙⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⣿⣧⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣒⣒⣛⣒⣒⣀⣀⣀⣤⣤⣤⣤⣀⣄⣉⣉⣉⣉⣀⣠⣦⣤⣤⣀⣀⣠ ⠀⠀⠈⠉⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⢹⡏⣷⡌⣩⣭⣩⣭⣍⡛⣛⣛⡻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠛⠁⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠉⣽⣾⣟⢸⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢀⣿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀ ⣠⣴⣆⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⠛⠻⠟⢃⣼⡯⠸⢿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡆⠀⠀⠀⢻⡇⠀⠀⠀⢀⠎⠐⠴⣾⣯⣽⣿⣾⣶⣿⣷⣤⣦⣤⣭⣥⣭⣭⣽⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡀⠀⠀⠀⢻⡆⠀⠀⠈⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⡇⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⡁⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⠀⠀⠀⢀⣀ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⢵ ⠘⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⢸⣦⠀⠈⠹⣆⣀⣠⣤⣤⣤⠠⠀⠀⣒⣲ ⠀⠘⢿⣿⣿⣿⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣃⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠘⣿⣿⣿⡇⠀⢀⣠⣤⣶⡾⠟⠛⠋⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠹⡿⢻⡽⠿⠛⠋⠁⠀⠀⠀⠀⠀⠰⣄⠀⣠⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣶⣄⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⠛⠿⣄⠀⢴ ⣷⠀⠀⠀⢠⣶⡄⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⡟⣻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠀⠀⠀⠀⣿⡋⠀⠀⠀⠀⠀⠉⠁⢀ ⣿⣷⡀⠀⢸⣿⣧⣥⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠐ ⣿⣿⡇⠀⢸⣿⢻⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⣿⣿⡇⠀⠈⡿⢸⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⡦⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⠀⠀⠇⢹⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⠀⣀ ⣿⣿⣿⠀⠐⠃⠚⠃⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⣾⣿ ⢹⣿⣿⡆⠀⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡍⠙⣦⣸⣿ ⣀⣻⣿⡇⢀⣿⣹⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠸⣿⡏⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⢀⣀⣀⣀⣀⣊⣀⣀⣤⣤⣤⣴⣶⣾⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣒⣲⣶⣖⣠⣀⣠⣀⣀⣠⣤⣄⣄⣀⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣠ 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⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⣿⣿⣿⡆⠀⣀⣠⣤⣶⠾⠟⠛⠃⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠹⡿⣛⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠰⣄⠀⣠⣴⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠁⢀⣴⣄⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠘⠛⢿⡂⠀⠀ ⣧⠀⠀⠀⢠⣦⡀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⡿⣻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠐⣶⡒⠀⠀⠀⠀⠀⠙⠁⠀ ⣿⣧⡀⠀⢸⣿⣿⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠰ ⣿⣿⡇⠀⢸⣿⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⣿⣿⡇⠀⠸⡏⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣦⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠀⠀⠃⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⣀ ⣿⣿⣿⠀⠐⠂⠚⠃⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣾⣿ ⢻⣿⣿⠀⠀⣷⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡍⢰⣤⣿⣿ ⣀⣿⣿⠀⢀⣯⣹⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⢸⣿⡌⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠲⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⡀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣤⣤⣤⣶⣾⣷⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣖⣖⣒⣀⣀⣒⣀⣀⣀⣀⣤⣄⣠⣀⣉⣁⣉⣁⣀⣀⣀⣋⣀⣄⢀⣤ ⠀⠀⠉⠉⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠸⡏⣷⡍⣩⣭⣩⣭⣍⡛⣛⣛⡻⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠀⠀⠀⣶⡇⠀⠀⠀⠀⠀⠀⠉⣽⣾⣟⢸⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢨⡅⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢺⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠀ ⣤⣴⡀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠛⠻⠟⢃⣼⣇⠸⢿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⠎⠀⠤⣾⣿⣿⣿⣶⣶⣿⣷⣦⣤⣤⣭⣥⣭⣭⣽⣛⣛⣛⣃⣻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ 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⣴⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠸⡏⣷⡌⣩⣭⣩⣭⣍⡛⣛⣛⡻⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⠃⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣟⢸⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢈⡇⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢺⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀ ⣤⣆⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠛⠻⠟⢃⣼⣇⠸⢿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡎⠀⠠⢤⣿⣿⣯⣴⣾⣿⣷⣦⣤⣤⣭⣥⣭⣭⣽⣛⣛⣛⣃⣻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡆⠀⠀⠀⢹⡇⠀⠀⠀⠀⠁⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⡀⠀⠀⠂⠀ ⣿⣿⣿⣿⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⣠⣶⣦⡀⠀⠀⠁⠀⠀⢨⠀ ⢻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠀⠀⢠⣄⣀⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠸⢾⢾ ⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣬⣤⣤⣶⣿ ⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⡄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣿⣿⣷⠀⢀⣀⣤⣶⡾⠿⠛⠋⠁⠁⠀⠀⠀⠈⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⠿⢟⡯⠿⠛⠛⠉⠀⠀⠀⠀⢀⠀⢳⣄⢀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢉⣭⣭⠉⠙⠭⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠛⠻⢇⡀⠀⠀ ⡄⠀⠀⠀⣶⣦⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢻⡟⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠈⠉⠀⠀ ⣿⣄⠀⠀⣿⣿⣤⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⢿ ⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀ ⣿⣿⠀⠀⢿⢸⣿⣿⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠸⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⢀⣤ ⣿⣿⡇⠀⠒⢐⡛⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿ ⣿⣿⡇⠀⢸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠉⣶⣼⣿⣿ ⣹⣿⣇⠀⣸⣍⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⢿⣿⠙⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠂ 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⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢈⡇⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢺⣿⣼⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀ ⣤⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⢀⠛⠻⠟⢃⣸⡇⠸⢿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣭⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣬⣿⣇⣴⢶⣿⣷⣦⣤⣤⣭⣥⣭⣭⣙⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⡿⢻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢹⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⢁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢰⣦⠈⠛⢧⣀⣠⣴⣶⣦⡄⠀⠀⠀⢀⡀⠀ ⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⣴⣿⣿⣿⣿⣛⣋⣀⣀⣀⣀⣠⣵⣿ ⠀⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢿⣿⣿⣧⠀⢀⣀⣤⣶⠿⠟⠛⠉⠀⠀⠁⠀⠀⠀⠉⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠿⠛⠣⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢦⣀⢀⣠⣶⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⡛⢿⠿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠉⠰⢥⡀⠀⠀⠀ ⠀⠀⠀⣶⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣛⠛⣻⢻⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⢀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⡄⠀⠀⣿⡇⣡⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀ ⣿⠀⠀⣿⢫⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⣿⠀⠀⠿⢸⣿⡿⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣧⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⣀⣤⣶ ⣿⡇⠀⠂⠀⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⠻⠀⢺⣿⣿⣷ ⣿⡇⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⣶⡾⣿⣋⣥ ⣿⡇⠀⣸⣈⣿⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⣿⣇⠈⢻⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠂⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠰⣾⠋⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣷⣶⣶⣶⣶⣖⣶⣲⣒⣲⣖⣲⣄⣤⣀⣀⣐⣄⣠⣄⣤⣤⣤⣀⣀⣠⣀⣠⣤⡀⣀⣀⣀⣤ ⠉⠁⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⢹⡏⣶⡌⣩⣭⣩⣭⣍⡛⣛⣛⡻⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣿⢸⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢨⣇⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀ ⡀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⡀⠛⠻⠟⢃⣼⡧⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠸⠅⠁⠀⢲⣷⣿⣧⣶⣶⣿⣷⣦⣴⣤⣭⣥⣭⣭⣝⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⡁⠀⠀⢀⠀⠀⠀ ⣿⣿⣧⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣶⡆⠀⠀⠀⠀⠀⠉⠀⠄⢀⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣾⣶⣤⣾⣿⠿⣄⠀⠀⠀⠀⠀⠀⠀⢰⠊⢂⠀⢀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⣿⣿⣿⢿⢒⣠⣤⣄⣀⡀⠀⠀⡠⠜⣁⣩⣴⣿ ⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣦⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢹⣿⣿⣿⡀⢀⣀⣤⣴⡾⠿⠛⠋⠁⠀⠈⠀⠀⠀⠀⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠻⠟⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠱⣤⡀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠿⠿⠿⢿⡿⣿⣿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠋⢡⢟⣔⠀⠀⠀⠀ ⠀⠀⣴⣶⠀⠀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⡛⢻⡟⣻⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀ ⠀⠀⢿⣿⣿⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀ ⡇⠀⢸⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀ ⡇⠀⠸⡇⣿⣿⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⡆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⣀⣤⣴⡶ ⣷⠀⠘⢐⣛⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣻⠃⢸⣿⣿⣿⡶ ⣿⠀⢸⡯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢲⡾⣿⣟⣯⣦ ⣿⠀⢘⣇⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⢿⣿⠈⠹⡿⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠐⢿⡏⠉⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⢀⣀⣀⣀⣀⣉⣃⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣶⣶⣷⣶⣶⣶⣿⣿⣿⣿⣯⣽⣽⣭⣵⣶⣦⣠⣤⣤⣤⣤⣤⣀⣀⣤⣠⣤⣖⣂⣄⣠⣤⣤ ⠉⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⢹⡏⣷⡌⣩⣭⣩⣭⣍⡛⣛⣛⡛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣿⢰⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢀⣶⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⢠⡄⠛⠻⠟⢃⣼⡧⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠿⠀⠀⢰⣶⣾⣿⣼⣿⣶⣿⣷⣤⣦⣤⣭⣥⣭⣭⣝⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⢋⠁⠀⠀⡀⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⡁⠀⠀⠀ ⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡄⠀⠀⠀⠘⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠀⢀⣠ ⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉⠉⠀⠰⣒⣄⣀⡀⠀⣠⣤⣤⠀⢌⣩⣴⣿⣿ ⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⣿⣿⣿⣇⠀⣀⣠⣴⣶⠿⠟⠛⠁⠀⠀⠉⠀⠀⠀⢈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠸⡿⠛⠷⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⣦⣄⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠶⣬⣭⠉⠀⠀⠀ ⠀⢠⣶⡆⠀⢀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣛⠛⣿⢻⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠋⠉⠀⠀⠀⠀ ⠀⢸⣿⣯⣧⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀ ⠀⠀⣿⢼⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀ ⠀⠀⣿⢸⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⢀⣠⣴⡶⠀ ⡆⠀⠃⣘⡃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣝⡟⠀⣿⣿⣿⡷⠀ ⡇⠀⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢐⣶⢿⣿⣿⣥⡖ ⡇⠀⣛⣰⣿⣆⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠸⣿⡇⠉⢿⠟⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣧⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠺⠿⠉⠁⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣷⣾⣶⣶⣶⣿⣿⣿⣿⣿⣭⣯⣽⣿⣭⣥⣥⣤⣤⣤⣤⣤⣤⣄⣀⣤⣄⣤⣴⣒⣀⣀⣠⣤⣤ ⠉⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⢹⡏⣶⡌⣩⣭⣩⣭⣍⡛⣛⣛⡛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣟⠰⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢀⣿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠀⠙⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢠⠄⠛⠻⠟⢃⣼⡗⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠯⠀⠀⢲⣶⣿⣷⣿⣷⣾⣿⣷⣴⣦⣤⣭⣥⣭⣭⣝⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢻⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢹⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⢠⠀⠀⠀⠀ ⣿⣷⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀ ⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠸⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠌⣇⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠁⠀⠠⠬⡁⠀⠀⠀⠀⠀⠀⠰⠈⠔⣠⣾⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⢶⣶⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿ ⠸⣿⣿⣿⡀⠀⣀⣠⣴⡾⠿⠛⠋⠁⠀⠀⠉⠀⠀⡀⢨⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠹⠟⢫⠽⠛⠛⠉⠀⠀⠀⠀⠀⠀⠐⣠⡄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠻⡽⣛⡛⠛⠉⠀⠀ ⠀⢰⣶⡄⠀⢠⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣛⠛⣿⢻⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠋⠁⠀⠀⠀⠀ ⠀⢸⣿⢿⣵⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀ ⠀⢸⡿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠘⠇⣿⣿⠟⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⡦⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡀⠀⢀⣠⣴⠆⠀ ⠀⠀⢀⣚⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡇⠐⣿⣿⣿⡆⠀ ⠀⢀⡗⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⢱⣦⢿⣿⣋⣤⠄ ⠀⢀⣏⣹⣿⣆⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⢸⣿⡌⠙⣿⠏⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠗⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠻⠏⠉⠁⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣀⣙⣉⣀⣀⣀⣀⣀⣀⣀⣠⣼⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣭⣽⣭⣭⣭⣵⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣠⣤⣶⣀⣀⣀⣀⣠⣤ ⠁⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠹⡏⣷⡌⣩⣭⣡⣭⣍⡛⣛⣛⡛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣟⠰⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢠⣿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢺⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠄⠛⠻⠟⠃⡸⣏⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣴⣾⣿⣿⣿⣾⣿⣿⣶⣶⣤⣤⣭⣥⣭⣭⣝⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢹⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢱⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ 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⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⠀⠀⣀⣤⡶⠀⠀ ⠀⠀⣐⡋⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⠀⢺⣿⣿⣷⠀⠀ ⠀⣽⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⣶⣾⣿⣛⣡⡄⠀ ⠀⣻⣙⣿⣦⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⣿⣏⠙⢻⡟⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠂⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⠿⠉⠁⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣬⣽⣷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⣒⣒⣢⣤⣤⣀⣀⣀⣀⣈⣉⣀⣁⣀⣨⣈⣉⣹⣒⣀⣀⣀⣀⣤⣤ ⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠹⡏⣷⡌⣩⣭⣡⣭⣍⡛⣛⣛⡛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣿⠐⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢰⣿⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠛⠻⠟⢃⢘⣯⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⠀⢠⣶⣾⣿⣿⣷⣿⣿⣿⣶⣶⣶⣦⣭⣥⣭⣭⣝⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢻⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢹⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠠⠀⠀⠀⠀⠀ ⣧⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⡀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠙⠉⠀⠀⠐⠂⢠⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠃⠀⠀⣠⣾⣿⣷⣶⣦⣤⣤⣄⣤⣬⣴⣾⣿⣿ ⣿⣿⣿⡀⢀⣀⣠⣴⣶⠿⠟⠋⠁⠀⠈⠉⠉⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⠟⠫⠼⠛⠛⠉⠁⠀⠀⠀⠀⠀⠸⣤⡀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠙⠉⠛⠛⠉⠻⣟⣿⡿⠿⠿⠿⠿⠿ ⣰⣦⡀⠀⣀⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡟⣻⠋⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⡀⠀⠀⠀⠀ ⢿⣿⣿⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀ ⢸⣿⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀ ⠘⡏⣿⣿⠟⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⣿⡟⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⡀⠀⢀⣠⣴⡆⠀⠀ ⠀⢃⣚⠃⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⠐⣿⣿⣿⡆⠀⠀ ⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢰⣶⣿⣟⣋⣤⠀⠀ ⢀⣟⣿⣿⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⢸⣿⡉⠻⣿⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠗⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡦⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠻⠯⠉⠁⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠈⢉⣡⣬⣥⣭⣭⣻⣿⣷⣒⣀⣀⣀⣠⣀⣤ ⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣶⠹⡏⣶⡌⣩⣭⣠⣭⣍⡛⣛⣛⡻⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣾⣟⠀⡇⢻⣿⣿⠇⣿⣿⠛⢃⣿⣿⣿⠀⣿⣿⣷⣦⢠⣶⣶⣦⡀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⢰⣧⢸⣿⡏⠀⣿⣿⠿⣸⣿⢻⣿⢠⣿⣿⣿⡟⢻⣿⣾⡛⠃⠀⠀⢀⣿⣿⣿⠀⣿⣿⢸⣿⠾⣿⣷⣶⢢⣴⣿⣥⡀⣤⣄⢀⣀⢀⣀⡀⠀⢀⠀⠀⠓⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠛⠻⠟⢃⣸⡧⠸⣿⠇⢰⣿⣷⣶⣿⣿⣿⣿⢸⣿⣧⣿⡇⣶⣽⣿⣿⠀⠀⠀⣸⣿⣹⣿⢰⣿⣿⣿⣿⠀⣿⣿⠀⣾⣿⢸⣿⡇⣿⣿⣼⣿⢸⣿⡇⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣭⣵⣭⣭⣝⣛⣛⣛⣃⡻⠿⠿⠟⣿⠆⢀⣿⣿⣻⣿⣼⣿⢻⣿⡇⠀⣿⡿⠀⣿⣿⣾⣿⢻⣿⣿⣿⡿⣼⣿⢹⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠈⠛⠃⠘⠛⠃⠀⠻⠿⠿⠟⢸⣿⢸⣿⡇⣿⣿⢸⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠉⠁⠀⠀⠐⢂⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣶ ⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣤⣤⣤⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣶⣶⣦⣥⣭⣵⣶⣿⣿⣿ ⣿⣿⣿⠀⢀⣀⣤⣴⡾⠿⠛⠋⠁⠀⠉⠉⠉⠁⠀⠐⣾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⠟⠩⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⢣⣤⡀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠻⣽⣟⡛⠛⠿⠿⠿⢿ ⣴⣦⠀⠀⣠⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣍⣽⢩⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢁⡀⠀⠀⠀⠀ ⣿⣿⢽⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀ ⢿⡟⣻⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⢹⡇⣿⣿⠛⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢁⣿⠋⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⣀⣤⣶⠆⠀⠀ ⠈⣒⡛⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⠃⢸⣿⣿⣿⡆⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⢳⣾⣿⣟⣫⣤⠀⠀ ⣸⣯⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⢿⣿⠙⠻⣿⠋⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠿⠏⠉⠁⢀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠉⠈⠉⠈⣉⣠⣬⣭⣭⣝⣿⣿⣗⣒⣀⣄⣀⣤⣀⣤ ⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀ ⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠯⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠀⠀⠀⠉⠠⢄⣀⣀⡀⠀⠀⠀⠀⠀⠠⠀⣀⣴⣿⣿ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣤⣤⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣇⠀⢀⣀⣤⣶⡿⠟⠛⠉⠀⠈⠉⠉⠉⠁⠀⢝⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠛⠽⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⢦⣄⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠳⣬⣉⠉⠙⠛⠛⠻⠿ ⣶⡄⠀⣀⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⡿⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣀⠀⠀⠀⠀⠀ ⣿⣿⣳⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠀⠀⠀⠀ ⣿⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⠿⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀ ⡿⢸⣿⡿⠋⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢸⡿⠃⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀⠀⢀⣀⣤⡶⠀⠀⠀ ⢐⢐⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⣿⣿⣿⣷⠀⠀⠀ ⣿⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡿⠙⣶⣿⣿⣛⣡⡄⠀⠀ ⣟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⡿⠿⠿⡿⠿⠿⠿⣿⣿⡿⠿⠿⠛⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡁⠀⣿⣏⠙⢿⡿⠁⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣴⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠘⣿⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠂⢻⡷⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⡇⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⠃⠀⢰⣿⣷⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣇⠻⣿⣷⣿⡟⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡄⠸⠿⠉⠁⠀⢀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣤⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣬⣉⣀⣀⣔⣀⣀⣀⣀⣄⣠⣤ ⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠽⠯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢀⣀⡀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠉⠁⠄⣀⣤⣀⡀⠀⠀⠀⠀⠠⢀⣠⣶⣿⣿⣿ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡀⠀⢀⣠⣤⣶⡿⠟⠛⠉⠈⠉⠉⠙⠛⠁⠠⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⢻⠽⠟⠛⠋⠁⠀⠀⠀⠀⠀⠸⣤⡄⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠶⣦⡄⠈⠉⠉⠙⠛⠛ ⣶⡀⠀⣀⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣀⠀⠀⠀⠀⠀ ⣿⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀ ⣿⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⠿⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⡿⢻⣿⡿⠉⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣻⡟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⢀⣠⣴⡖⠀⠀⠀ ⣒⣚⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡇⠀⣿⣿⣿⡧⠀⠀⠀ ⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢱⣶⣿⣿⣛⣥⠀⠀⠀ ⣟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⡀⠸⣿⡏⠛⣿⠟⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣶⣶⡆⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠸⣇⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠂⢿⠗⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⡇⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠀⣾⣿⣦⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣧⠻⣿⣷⣿⡟⣸⣿⡸⣿⣷⣿⡿⠃⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⠺⡿⠋⠁⠀⠀⢀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣶⣶⣶⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣒⣂⣀⣀⣀⣀⣠⣠⣤⣤⣤⣌⣉⣤⣤⣐⣀⣀⣤⣠⣄⣀⣠ ⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠽⠯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀⣀⡀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠉⠠⢄⣠⣄⣀⠀⠀⠀⠀⠀⠠⣀⣤⣾⣿⣿⣿ ⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡀⠀⣀⣠⣤⣶⡿⠟⠛⠁⠈⠉⠉⠙⠛⠀⠤⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⢻⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠰⣤⡀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⢶⣄⡄⠉⠉⠉⠛⠛⠛ ⣶⡀⠀⢀⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢃⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⣿⣼⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⠟⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⠟⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⢀⣠⣴⡆⠀⠀⠀ ⠂⠚⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⣿⡇⢸⣿⣿⣿⡆⠀⠀⠀ ⣯⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢳⣾⣿⣟⣫⣤⠀⠀⠀ ⣟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⡀⠸⣿⡉⠻⣿⠏⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠹⡇⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⢠⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠃⣿⠗⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢣⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⡇⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠸⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠀⣾⣿⡄⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣇⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠃⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠉⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⠾⣟⠉⠁⠀⢀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣌⣉⣠⣤⣀⣀⣤⣤⣤⣤⣀⣬ ⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠽⠭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⣀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠀⠀⠉⠀⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⣀⣠⣴⣶⠿⠟⠛⠁⠉⠉⠉⠛⠛⠀⠤⢟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠫⠽⠟⠛⠉⠁⠀⠀⠀⠀⠀⢰⣤⡀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠱⢶⣄⡌⠉⠉⠙⠛⠿⠿ ⣆⠀⠀⣀⣤⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃⡀⠀⠀⠀⠀⠀ ⣿⣺⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀ ⣟⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⠟⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⠟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣄⠀⠀⢀⣠⣴⡆⠀⠀⠀ ⡒⠚⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⡇⢸⣿⣿⣿⡆⠀⠀⠀ ⣯⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢲⣾⣿⣟⣫⣤⠀⠀⠀ ⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⡿⠿⠿⡿⠿⠿⠿⣿⣿⡶⢶⡤⡤⢠⣤⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⡀⠻⣿⡉⠻⣿⠏⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣧⠁⣿⣿⡇⣿⣿⠹⢻⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠹⡇⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠃⣿⠆⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡀⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⡿⠃⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⠠⣶⣿⡄⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣇⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⢾⣟⠋⠁⠀⠀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣌⣉⣠⣄⣤⣤⣤⣄⣤⣀⣀⣨ ⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠯⣭⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣴⣿⣷⣦ ⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿ ⣿⣧⠀⠀⣀⣤⣴⣾⠿⠛⠋⠀⠉⠉⠙⠛⠛⠀⠤⣟⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠫⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⢧⣀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠈⠙⠭⣭⣉⠝⠛⠛⠿⢿⣿⣿ ⣆⠀⠀⣀⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠂⠀⠀⠀⠀⠀⠀ ⣿⣂⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀ ⡏⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠀⠀ ⠸⣿⣿⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⠃⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⣀⣤⣶⠀⠀⠀⠀ ⡀⠓⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⠀⢺⣿⣿⣿⠄⠀⠀⠀ ⣏⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣭⣿⣿⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣶⣾⣿⣟⣩⡄⠀⠀⠀ ⣿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⠿⠿⠿⠿⠟⠛⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣃⡀⢿⣿⠙⢻⡿⠃⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣴⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠹⡄⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠓⣿⠆⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⡿⠁⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⠃⠠⣾⣷⡄⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⡿⣿⣇⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡄⢾⠟⠋⠀⠀⠀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣌⣉⣠⣤⣤⣦⣤⣄⣤⣀⣀⣨ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠼⢭⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠒⠂⠀⠀⠐⠂⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣴⣤⣄ ⣿⡆⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⣿⣶⣶⣶⣶⣬⣥⣥⣶⣿⣿⣿⣿⣿ ⣿⣷⠀⢀⣀⣤⣶⡾⠿⠛⠋⠀⠈⠉⠉⠛⠛⠀⠴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⡫⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⢧⣀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠈⠻⢍⣙⣛⡛⠿⡿⣿⣿⣿⣧ ⣆⠀⠀⣀⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⠀⠀⠀⠉⠉⠉ ⣿⢰⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀ ⡏⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠟⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⠋⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠏⠀⠀⠀⠀⠀⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⣀⣤⣶⠀⠀⠀⠀ ⡊⡛⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⠀⢺⣿⣿⣿⠄⠀⠀⠀ ⡏⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣶⣾⣿⣟⣫⡄⠀⠀⠀ ⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣁⡀⢿⣿⠙⢿⡿⠃⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠹⠀⠈⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡆⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠓⡷⠂⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⡇⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⠃⢰⣾⣷⡄⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣧⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢻⠇⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡆⢿⡛⠉⠀⠀⣀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣬⣷⣶⣾⣷⣶⣶⣶⣶⡿⠶⠶⢶⣦⣤⣀⣀⣀⣀⣤⣤⣤⣤⣈⣉⣤⣤⣤⣶⣤⣤⣤⣤⣀⣠ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠽⣭⣻⣿⣿⣫⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢉⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠖⠒⠀⠀⠀⠀⠀⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤ ⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣶⣦⣶⣤⣭⣭⣥⣴⣾⣿⣿⣿⣿ ⣿⡇⠀⢀⣀⣤⣶⠾⠿⠛⠉⠀⠉⠉⠙⠛⠛⠠⢴⣾⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠡⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢦⣄⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠊⠻⢍⣛⣛⠻⠿⣿⣿⣿⣿⣯ ⡄⠀⠀⣀⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣀⠀⠀⠈⠉⠉⠉ ⣧⢢⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀ ⣏⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡿⠛⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡿⠋⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡿⠃⠀⠀⠀⠀⠀⠡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀⠀⠀⣠⣤⡶⠀⠀⠀⠀ ⠚⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣽⣿⠀⣿⣿⣿⣷⠀⠀⠀⠀ ⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠁⣶⣿⣿⣟⣥⡀⠀⠀⠀ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⣿⣿⣿⣿⡿⠿⠿⣿⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣁⡀⢿⡏⠛⢿⡿⠁⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠟⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⠇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠳⡷⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠉⠉⠀⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢴⣿⣧⠀⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣧⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⢾⠛⠉⠀⠀⣀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣄⣀⣀⣤⣠⣤⣤⣈⣉⣤⣤⣤⣦⣤⣤⣤⣄⣀⣤ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀ ⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠹⠿⣿⣿⣿⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⠀⠀⠀⠈⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤ ⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣾⣷⣶⣦⣤⣤⣤⣠⣤⣤⣴⣾⣿⣿⣿ ⣿⡇⠀⢀⣀⣤⣶⠾⠿⠛⠉⠈⠉⠉⠙⠛⠻⠤⢴⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠟⠩⠿⠛⠋⠁⠀⠀⠀⠀⠀⠘⣤⣄⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠵⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠏⠙⢿⣛⣛⠿⠿⣿⣿⣿⣿⣿ ⡄⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⡀⠀⠀⠈⠉⠛⠛ ⣇⣢⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⠈⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⡀⠀⢀⣠⣤⡆⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣶⣿⠿⠟⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡟⠀⣿⣿⣿⣧⠀⠀⠀⠀ ⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢁⣶⣿⣿⣛⣥⠀⠀⠀⠀ ⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡿⠿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣁⡘⢿⡏⠛⣿⠟⠀⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠋⣿⣿⡇⢿⡿⠁⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠳⠶⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⠁⢴⣿⣦⠀⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣧⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡄⣾⠛⠁⠀⠀⢀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠂⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣀⣀⣀⣀⣀⣤⣤⣤⣤⣈⣉⣄⣤⣴⣦⣦⣤⣤⣀⣠⣤ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠛⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣰⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠤⠄⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀ ⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣶⣶⣤⣤⣤⣤⣒⣐⣀⣤⣶⣿⣿⣿ ⣿⡆⠀⣀⣠⣤⣶⠿⠟⠛⠉⠈⠉⠉⠙⠛⠛⠆⢰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠹⠟⠛⠋⠁⠀⠀⠀⠀⠀⠰⣤⡀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠵⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠙⢿⡛⠿⠿⢿⣿⣿⣿⣿⣿ ⡄⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⠀⠀⠀⠉⠙⠻⠿ ⡇⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣟⠛⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⠈⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡀⠀⢀⣠⣴⡆⠀⠀⠀⠀ ⠛⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡇⢰⣿⣿⣿⡧⠀⠀⠀⠀ ⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢱⣾⣿⣿⣛⣥⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣀⡘⢿⡏⠛⣿⠟⠀⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⡄⣿⣿⡇⣴⣦⡄⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠳⠶⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⡇⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⢴⣿⣦⠀⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣇⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠃⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⣿⡛⠃⠀⠀⠀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⡇⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣶⣶⣿⣷⣶⠾⠷⠶⠶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣈⣉⣄⣤⣴⣶⣦⣤⣤⣄⣀⣀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠛⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣸⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠄⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀ ⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣶⣶⣤⣤⣤⣤⣒⣐⣀⣤⣶⣿⣿⣿ ⣿⡆⠀⢀⣠⣤⣶⠿⠟⠛⠉⠈⠉⠉⠙⠛⠛⠆⢐⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠹⠿⠛⠛⠁⠀⠀⠀⠀⠀⠰⣤⣀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠵⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠙⢿⡛⠿⠿⢿⣿⣿⣿⣿⣿ ⡄⠀⢀⣀⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⠀⠀⠀⠉⠙⠛⠿ ⡗⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣟⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠙⠷⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠙⢿⡛⠿⠿⣿⣿⣿⣿⣿⣿ ⡄⠀⢠⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣆⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠉⠛⠻⠿ ⣇⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⣹⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡟⠛⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠈⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⠈⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀ ⠛⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣽⡇⢰⣿⣿⣿⡇⠀⠀⠀⠀ ⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢱⣾⣿⣿⣛⣥⠀⠀⠀⠀ ⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⣀⡸⢿⠛⠻⣿⠟⠀⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣴⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⡆⣿⣿⡇⣶⣶⡄⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⣿⣿⡇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠓⠖⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⡇⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⣾⣿⣆⠀⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣧⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢹⡇⣿⣿⢀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⣟⠛⠁⠀⠀⠀⢀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⡇⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣉⣀⣲⢿⡷⢶⠾⠷⠶⠶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣈⣉⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀ ⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠸⢿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠄⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⣆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣤⣤⣤⣤⣤⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣵⣶⣶⣤⣤⣤⣀⣒⣀⣀⣀⣤⣶⣿⣿ ⣿⠀⠀⣀⣠⣴⡶⠿⠟⠋⠁⠈⠉⠉⠛⠛⠛⠧⢐⣺⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢰⣤⡀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⡿⠛⢿⡻⠿⠿⣿⣿⣿⣿⣿⣿ ⡄⠀⣀⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡎⣺⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠉⠛⠿⠿ ⡍⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡟⠛⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠀⠀⠀⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⠀⠀⢀⣠⣴⠆⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣯⣿⠇⢸⣿⣿⣿⡆⠀⠀⠀⠀ ⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢲⣾⣿⣿⣫⡤⠀⠀⠀⠀ ⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡶⠶⣾⣿⣷⣶⡶⠶⠶⣶⣶⠤⠀⣶⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣀⡹⠿⠙⢻⡿⠇⠀⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠋⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⠇⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠃⠆⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⣾⣷⡄⠀⠀⠀⢀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣇⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⣟⠛⠀⠀⠀⠀⢀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⡇⠀⢀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣄⣀⣀⣀⣀⣀⣄⣀⣀⣤⣤⣤⣤⣈⣉⣤⣤⣴⣶⣶⣦⣤⣤⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠘⠫⣭⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣼⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠄⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣶⣦⣤⣀⣀⣀⡀⢀⡀⣀⣠⣴⣾⣿ ⣿⠀⠀⣀⣠⣴⡶⠿⠛⠋⠁⠉⠉⠉⠛⠛⠛⠧⢐⣺⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠾⠿⠛⠋⠀⠀⠀⠀⠀⠀⢢⣄⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⠻⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿ ⡀⠀⣠⣤⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡎⣺⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⠀⡀⠉⠙⠛⠿⢿ ⣍⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠈⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠀⠀⠀⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⢀⣤⣴⠂⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣯⣿⡇⢸⣿⣿⣿⡆⠀⠀⠀⠀ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡋⢱⣾⣿⣿⣫⣤⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣶⣶⣶⣶⡶⠾⠟⠋⠉⠙⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣀⡹⠿⠙⢻⣿⠇⠀⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠏⣿⣿⡇⣿⣿⠃⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠻⠛⠀⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠃⠆⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⣾⣷⡄⠀⠀⠀⢀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣧⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⠀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⣟⠛⠀⠀⠀⠀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⡇⠀⢀⣀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣀⣠⣤⣤⣤⣤⣈⣉⣤⣤⣴⣶⣶⣦⣤⣤⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣦⣤⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠙⣻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣰⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⡻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣢⣤⣤⣀⣀⣀⠀⠠⠄⠀⠀⣀⣤⣶⣶ ⣧⠀⢀⣀⣠⣴⡾⠿⠛⠋⠁⠉⠉⠉⠙⠛⠛⠗⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⢢⣤⣀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⣠⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⢃⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠒⠀⠀⠉⠙⠻⢿⣿⣿ ⡅⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡛⠙⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡄⠀⠀⣀⣤⣶⠀⠀⠀⠀⠀ ⠛⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣿⠀⢸⣿⣿⣿⠄⠀⠀⠀⠀ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣶⣾⣿⣟⣯⡄⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⣀⡻⠟⠙⢿⡿⠃⠀⠀⠀⠀ ⣿⢹⣿⣿⣿⡇⣿⣿⣿⣿⡆⣼⣿⡿⣿⣷⢹⣿⢰⣿⡿⣿⣷⢸⣿⣿⣿⣿⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣧⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⢸⣿⡇⣴⣿⡿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⣤⡄⣿⣿⣧⣿⡇⣿⣿⡇⣿⣿⢸⣷⠸⣿⣷⣭⡉⠄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠁⣿⣿⡇⣿⣿⡆⣿⣿⣤⡄⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣇⣛⣛⠃⠂⠀⠀⠀⠀⠀⠀ ⣿⢸⣿⣿⠛⠃⣿⣿⣟⣛⡁⣿⣿⡇⣿⣿⢸⣿⢡⣬⡟⣿⣿⡄⢸⣿⣿⠀⢸⣿⣿⢸⣿⡇⠀⣿⣿⡇⢿⣿⡇⣿⣿⠛⢳⣿⣿⣿⣿⡆⣿⣿⡇⣿⣿⠀⢸⣿⣿⢸⣿⡿⣿⣿⡇⣿⣿⡟⣿⣿⡇⣾⣷⡄⠀⠀⠀⠀ ⣿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣧⠻⣿⣷⣿⡿⣸⣿⡸⣿⣷⣿⡿⠁⢸⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣀⣸⣿⡟⢻⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⡇⢻⣿⡇⠻⣿⣷⣿⣿⡇⠛⠋⠀⠀⠀⠀⣀ ⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⣷⣶⣿⣷⣾⣿⣿⣿⣶⣿⣷⣶⡇⢀⣀⣀⣀⣴⣦⣶⣦⣤⣤⣤⣤⣤⣐⣺⣿⣿⣶⣶⣿⣷⣶⣾⣶⣤⣤⣤⣀⣀⣀⣄⣀⣀⣀⣀⣤⣀⣠⣤⣤⣤⣤⣈⣉⣤⣤⣴⣶⣦⣤⣤⣤⣠⣤ ䷩ 𝚕𝚒𝚗𝚎 1051 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/07/epo-going-after-pensioners/#comments Gemini version at gemini://gemini.techrights.org/2022/01/07/epo-going-after-pensioners/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ The_EPO’s_Race_to_the_Bottom_—_Part_V_—_An_Assault_on_Pensioners⠀✐ Posted in Deception, Europe, Finance, Patents at 6:22 am by Dr. Roy Schestowitz They’re going after pensioners, as_we_noted_almost_exactly_a_year_ago, based on leaks Series parts: 1. The_EPO’s_Race_to_the_Bottom_—_Part_I_—_From_Bad_to_Worse 2. The_EPO’s_Race_to_the_Bottom_—_Part_II_—_“Playing_People_Off_Against_Each Other_is_Not_the_Way_We_Want_to_Go_Forward!” 3. The_EPO’s_Race_to_the_Bottom_—_Part_III_—_“The_King_is_Naked”_(a_Fake Financial_Shortage_and_‘Missing’_—_or_Plundered_—_Billions) 4. The_EPO’s_Race_to_the_Bottom_—_Part_IV_—_New_Career_System_(NCS)_and_New Pension_System_(NPS) 5. YOU ARE HERE ☞ An Assault on Pensioners 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇Woman ready to fight with clenched fists⦈ Europe’s second-largest institution is deeply corrupt and managers are fighting their own. EPO has become a_money-hoarding_institution, monetising invalid patents that are granted by the bucketloads to multinational corporations that are neither European nor deserving of these European Patents Summary: Benoît_Battistelli, who was put in charge of the EPO despite being in retirement age (it’s not supposed to be done), has declared war not only on EPO staff but also former (and retired) EPO staff; António_Campinos, who is ‘finishing the job’, has absolutely no grasp of how to run a patent office (he never did this kind of thing before) TWO years ago the union of EPO staff published and then circulated some material about EPO pensions and retirement age — seemingly ‘superficial’ things until one realises that in order to attract talented examiners the Office must offer something competitive (compared to the public and private sector). The EPC makes this very clear; what good is a patent office that hands out loads of invalid monopolies, potentially due to improperly-skilled workers? “There’s no desire to reward staff for hard work or attract the necessary examiners, who are equipped with the required knowledge level.”25 months ago SUEPO published the following article about a “bombshell” — not literally a bomb but another heart-sinking revelation. They take note of the elusive retirement age — the threshold many perceive to be a personal liberation from a long life of work (in some cases about 50 years of nonstop work). We’re reproducing it below as HTML: 18.11.2019 su19025mp – 0.2.1 § Mr Campinos’ 17 measures⠀➾ ––––– § Planned change of retirement age⠀➾ § Consequences on early pension level⠀➾ Dear SUEPO members, dear colleagues, Mr Campinos revealed his bombshell, i.e. the “17 measures”, a few weeks ago. The Staff Representation has already explained why the future financial “gap” was in fact an artificial construction by top management. It remains that many colleagues above or approaching 50 look at all potential measures affecting pensions very carefully. One measure in particular worries many: the change of retirement age. Staff are concerned that adequate transitional measures that should normally protect their acquired rights and legitimate expectations may not be part of any measure concerning the change of pension age. They are also worried that they may get trapped and be too late to “jump off the boat”, should they decide to leave the Office on (early) pension. Let’s have a look at the measures contemplated by management. Page 136 of the consultant’s report (CA/83/19) gives a precise idea of where Mr Campinos intends to go. We have translated the three scenarios “Low”, “Medium”, “High” mentioned under the header “gradually increase retirement age” into the annexed tables by using exclusively the information provided on page 1361. We did not make any assumption. A quick look at the annexed tables shows that in all scenarios: - The change is sudden; - Only colleagues becoming 61 or older in 2021 (born in 1960 or earlier) are not affected; - The right to an early pension of all colleagues reaching the age between 50 and 60 in 2021 (born between 1961 and 1971) is (enormously) affected (cf. coloured area of the tables), many being even prevented from taking an early pension for several years after 2021. In fact, the so-called “gradual” increase is so steep and affects staff close to the current retirement age of 60 in such a sudden way that it cannot be decently described as a transitional measure2. The loss of (early) pension rights is huge for a large part of the EPO staff: for instance, colleagues born in 1964, 1965 or 1966 loose a fifth (!) of their early pension with the contemplated change (both in the High and Medium scenario)3. To recover the same level of _________ 1 i.e. the “transitional” approach used by the consultant and the “shift [of] existing 10-year early retirement window & existing early retirement factor scale accordingly.“ 2 The increment of pension age chosen by management for their “transition” is of one year, whereas increase of pension age should be small and truly_gradual, e.g. be of one month per age difference of one year and not affect colleagues being already in a position to exert their right to an early pension, so that no one is trapped/ surprised in an unlawful way. 3 Colleagues born in 1966 lose 23% of their early pension (compare 0.77 and 0.54 both in High and Medium scenarios). Colleagues born in 1964-1965 lose 20% of their pension (compare 0.81 and 0.61, resp. 0.85 and 0.65, both in High and Medium scenarios) ===================================================================== early pension they are currently entitled to, they would have to work another three or four (!) long years at the EPO. Considering the depressing atmosphere and insane work pressure in the Office, we can safely predict that, should management stick to their brutal plans, a large number of colleagues will leave on early pension in 2020. This bring us to the question of when to “jump off the boat” for those who can. Article 54 ServRegs currently requires active staff to inform the Office in writing at least 6 months before the start of their retirement4. Article 9 of the Pensions Regulations states that “Entitlement to payment of a retirement pension shall commence on the first day of the month following that in which the employee became eligible for such pension.“ The latest possible date for the start of a pension before 1 January 2021 is therefore 1 December 2020. Consequently, according to the regulations currently in place, the latest possible working day to inform the Office of a retirement starting in December 2020 is Friday_29_May_2020. Mr Campinos stated in his communiqué_of_4_June_2019: “[...] any proposals we put to the Council will include provisions that safeguard the right of our colleagues to have enough time to make well informed and timely decisions concerning their future, should they wish to. If we have to introduce transitory measures to give our staff enough time to make a decision, then that is what we shall do.” In a meeting with SUEPO the day before (3 June) the President had been more specific. He suggested that a possible transitional measure could be a temporary shortening of the notice period from 6 to 3 months after 1 July 20205. This would mean that staff willing to go on early pension before the end of 2020 could inform the administration after May (and July) 2020. The question remains whether these written and oral statements of Mr Campinos actually commit the Office in practice6, and whether such a change of notice period will indeed be part of the reform package submitted to the Administrative Council of June 2020. Depending on whether or not staff trusts management, will determine the latest date at which they will decide to inform the administration that they are leaving on early pension. The above are individual strategies to avoid future harm. The best way to make sure that the changes proposed by Mr Campinos in his 17 measures, including the increase of retirement age, are stopped or made respectful of staff’s (acquired) rights, is to collectively act against them. The mobilisation in the coming weeks/months will be crucial. Your SUEPO Munich Committee _________ 4 Art. 54(2) reads: An employee shall inform the Office in writing of the concrete date of commencement of his retirement and annual leave plans at least six months prior to the requested starting date of retirement. [...] 5 Cf. SUEPO publication su19030cp (§5) 6 Mr Campinos recently broke his promise made to the CSC to allow the CSC to run the 4th edition of the Technologia Staff Survey on Office channels, cf. CSC publication sc19131cp. 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇EPO_retirement_table⦈_ Separately, in this_presentation [PDF], SUEPO said: “There is no financial GAP but a surplus. Let’s meet with Mr Campinos in the middle of the bridge and discuss measures on how to distribute the surplus to the staff.” Here’s the above explained using slides: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_1⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_2⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_3⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_4⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_5⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_6⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_7⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_8⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_9⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_10⦈_ 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇Find_the_GAP_presentation_page_11⦈_ A lot of what’s in the above presentation is still relevant, never mind the age. The plan of EPO management has not changed; they just talk about how and when to implement it. So yes, it’s a race to the bottom. There’s no desire to reward staff for hard work or attract the necessary examiners, who are equipped with the required knowledge level. █ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠂⠈⠉⠁⠈⠀⠈⠉⠙⠉⠁⠀⠉⠛⠛⠻⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣝⣽⡆⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣄⡀⠀⢀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠁⣾⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢹⣿⡏⣿⣿⢩⣭⣭⣭⡍⣭⣭⢩⣭⡍⣭⣭⢩⣭⣭⣭⡍⣭⣭⢩⣭⡍⣭⣭⣭⣭⢹⣿⡏⣿⣿⢹⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣗⢒⢸⠶⡃⡗⢾⢀⠒⣿⡐⡂⡗⢒⢸⠲⡃⡒⢺⢀⠒⣿⠐⡂⡗⢒⢐⠒⡇⡐⢺⣇⠒⢸⡒⡃⡷⢾⢐⠒⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠿⡿⠟⡟⠟⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣒⢸⣂⡂⣏⣹⢀⣀⣿⣐⡀⣇⣂⢸⣑⡆⣊⣼⢀⣀⣿⣒⡀⣇⣐⢰⣁⡇⣂⣸⣇⣂⢸⣐⡃⣗⣺⢸⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣭⣭⢨⣭⡅⣭⣭⢨⣭⣭⣭⡅⣭⣭⢨⣭⡅⣭⣭⢨⣭⣭⣭⡅⣭⣭⢨⣭⡅⣭⣭⣭⣭⢨⣭⡅⣭⣭⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⠻⢸⠛⠇⡟⣻⠘⠛⣿⠛⠃⡟⠛⢸⢟⡇⡻⣻⠘⠛⣿⠛⠃⡟⠛⢸⢟⡇⠻⢻⡟⠛⢸⠛⡇⡟⢻⢸⠻⣿⣿⣿⢻⠿⢿⠻⢿⡻⠻⡻⢻⣟⠿⠻⠿⢿⠻⠻⠟⠿⢿⠿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣤⢸⣮⡇⣿⣾⢠⣤⣿⣤⡄⣧⣤⢸⣮⡆⣦⣾⢠⣤⣿⣤⡅⣧⣴⢰⣮⡇⣼⣾⣧⣤⢸⣥⡆⣧⣼⢸⣯⣿⣿⣿⣶⣼⣾⣶⣾⣶⣶⣶⣾⣧⣾⣷⣶⣿⣶⣾⣶⣷⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⣛⣛⢘⠛⡃⡛⢛⢘⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⠸⠄⡇⠧⢸⠸⠌⣿⣿⣿⠩⠛⠛⠉⡟⠛⢛⠙⣻⢛⠛⡛⠋⢛⣻⡟⣻⠍⠉⠍⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠭⢸⠭⡇⡯⢼⠀⠥⣿⠠⠄⡇⠬⢸⠤⡇⠥⢼⠀⡤⣿⠠⠄⡇⢬⠸⡤⡇⠠⢼⡇⠤⢸⠀⡇⣇⢸⢐⢐⣿⣿⣿⣿⣿⡟⠿⠛⠿⠿⡟⠿⠟⠻⠟⠿⠿⠿⡿⠻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣇⣀⢸⣀⡇⣇⣸⢀⣀⣿⣀⡀⣇⣀⢸⣢⡇⣑⣸⢨⣂⣿⣀⡀⣗⣲⢸⣜⡇⣂⣸⣇⣂⢸⠀⠃⡇⢸⢨⠈⣿⣿⣿⣿⣿⣷⣶⣶⣶⠾⠷⠷⠷⡶⢶⠶⢾⠷⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣀⡅⣇⣸⢘⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣤⣤⣤⣥⣤⣧⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⣶⢰⣶⡆⣶⣶⢰⣶⣶⣶⡆⣶⣶⢰⣶⡆⣶⣶⢰⣶⣶⣶⡆⣶⣶⢰⣶⡆⣶⣶⣶⣶⢰⣶⡆⣶⣶⢰⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⠻⠻⠻⡻⠻⠻⠻⡟⠻⠿⠿⠻⠿⢿⠿⠿⢿⠿⡟⠽⠍⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⡨⢸⠋⠅⡷⢿⠈⠈⣿⠡⠁⡇⠌⢸⠢⡅⠕⢹⠨⠨⣿⠁⠅⡇⠨⢨⢂⡇⠅⢹⡏⠨⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣷⣶⣷⣶⣶⣶⣶⣷⣷⣶⣶⣶⣶⣾⣶⣴⣾⣶⣷⣾⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣅⣉⣈⣉⣡⣌⣋⣹⣀⣉⣭⣉⣉⣀⣄⣉⣉⣍⣙⣹⣂⣀⣄⣔⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠿⠿⠸⠿⠇⠿⠿⠸⠿⠿⠿⠇⠿⠿⠸⠿⠇⠿⠿⠸⠿⠿⠿⠇⠿⠿⠸⠿⠇⠿⠿⠿⠿⠸⠿⠇⠿⠿⠸⠿⠇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⡏⢩⢸⠉⡇⠉⣹⡏⢩⢸⠉⡅⡏⢹⢸⠉⣿⣿⣿⢟⠿⠿⠛⡿⠿⠿⠻⢿⠿⠿⠿⠟⠿⢿⡿⢿⡟⠟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⣛⢸⣛⡇⣟⣻⢘⠛⣿⠛⠃⡟⢛⢸⠛⡇⡛⢻⠘⠛⣿⠛⠃⡅⢸⠨⠀⡇⠄⢿⡇⢸⢨⠀⡇⡅⢸⠨⠨⣿⣿⣿⢶⡶⣶⣶⣷⣶⣾⣦⣿⣶⣶⣷⣶⣶⣿⢷⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⡪⢸⢛⠅⣟⢻⠈⠁⣿⠈⠁⡇⠭⢸⠉⠇⠅⢹⠠⠩⣿⠨⠅⡇⢸⢘⢀⡇⡀⣹⡇⣸⢸⢀⡇⡇⣸⢈⣈⣿⣿⣿⣠⣤⣤⣤⣧⣤⣴⣤⣤⣤⣍⣧⣤⣤⣥⣺⣥⣥⣶⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⡇⢐⢨⠂⡇⠐⣸⡇⢐⢸⠀⡆⡗⢸⢨⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣩⣹⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣛⣛⣘⣛⣃⣛⣛⣘⣛⣛⣛⣃⣛⣛⣘⣛⣃⣛⣛⣘⣛⣛⣛⣃⣓⣚⣐⣒⣃⣒⣚⣓⣚⣘⣓⣃⣓⣚⣐⣒⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢍⣽ ⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿ ⣿⡟⢛⢸⡛⡇⣟⢻⠘⡛⣿⠛⡃⡟⢛⢸⡛⡇⣛⢻⠘⡛⣿⠛⡃⣟⢛⢘⡛⡇⢛⢻⡟⢛⢸⡛⡇⣟⢻⢘⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠨⣿ ⣿⡗⣒⢸⡚⡂⡧⢿⠐⠐⣿⢂⠂⡇⡐⢸⢌⡂⡢⢸⠐⠐⣿⣂⠂⡇⢐⢘⠄⡇⡒⢺⡗⡂⢸⢚⡆⣗⣻⢰⢒⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣉⣉⣏⣁⣇⣁⣁⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠜⣿ ⣿⠷⠶⠸⠶⠆⠷⠾⠰⠶⠿⠶⠆⠷⠶⠸⠶⠇⠶⠿⠰⠶⠿⠶⠆⠷⠶⠸⠶⠇⠶⠾⠷⠶⠸⠶⠆⠷⠾⠸⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣗⡒⣾ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣹⡇⡀⣿ ⣿⡇⠀⢸⡰⡇⣧⣺⠀⠀⣿⠀⠀⡇⠀⢸⡱⡃⡊⣺⠀⠀⣿⠀⠄⡇⢂⢐⡱⡇⢢⣸⡇⠀⢸⠄⡃⡇⢸⢸⡤⣿⣿⣿⣘⢩⣹⣈⣹⣊⣈⣊⣸⡗⣩⣌⣉⣽⣈⣨⣁⣍⣙⣉⡁⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡗⠂⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⠉⡇⡏⢹⢸⠙⣷⣿⣿⠿⢿⢿⠿⡿⡿⡿⢿⣿⢿⢿⢿⡿⢿⢿⣿⢿⠿⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣯⠀⣿⣇⡀⣿ ⣿⡟⠿⢸⠿⡇⡿⢻⠘⠟⣿⠛⠃⡟⠻⢸⠛⡇⠟⢻⠘⠛⣿⠛⠃⡟⠻⢸⠛⡇⠛⢻⡟⠛⢨⠀⡇⡅⢸⢈⢀⣿⣿⣿⣬⣴⣴⣤⣧⣤⣶⣤⣾⣵⣤⣦⣦⣴⣾⣷⣾⣥⣤⣤⣭⣿⣿⣿⣿⠉⣿⣿⣿⡀⣿⡯⠤⣿ ⣿⡇⠉⢸⠉⡇⡏⢹⠀⠉⣿⠈⠁⡇⠉⢸⡉⠇⠌⢹⠠⠋⣿⠈⠁⡇⢙⢨⢫⡇⡈⢹⡇⠉⢸⠠⡇⡇⢼⠠⠤⣿⣿⣿⣿⣿⣇⣉⣀⣉⣩⣇⣍⣅⣈⣁⣉⣩⣍⣋⣌⣹⣹⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣇⢀⣿ ⣿⣷⣶⢸⣶⡇⣷⣾⢸⣶⣿⣶⡆⣷⣾⢸⣾⡇⣿⣿⢸⣷⣿⣶⡆⣿⣿⢸⣷⡇⣷⣾⣷⣿⢸⠀⠄⡇⢸⢸⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⠉⠉⠉⠏⠙⡍⡽⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠥⣿⡧⠴⣿ ⣿⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⣛⣛⢘⣒⡃⣓⣚⢐⣒⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢻⣿⣤⣿⣿⣿⠀⣿⡧⡀⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⢸⣿⣿⣿⣿⣿⢉⣹⣏⢀⣿ ⣿⡟⠻⢸⠛⠇⡟⣻⠸⠛⣿⠛⠇⡟⠻⢸⠛⠇⠟⣻⠘⠛⣿⠛⠇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣌⣈⣌⣊⣈⣈⣈⣇⣌⣉⣉⣈⣉⣹⣉⢉⣹⣉⣇⣩⣈⣿⣿⢸⣿⣿⣿⣿⣿⠀⢺⣗⢑⣿ ⣿⣧⣮⢸⣤⡅⣯⣽⢠⣥⣿⣬⡄⣧⣭⢸⣭⡇⣭⣽⢨⣬⣿⣥⡅⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⡟⠿⠛⠿⠛⠻⠿⢻⠛⠿⠿⠟⠿⠛⡛⠿⠿⠿⢟⢿⡛⠛⠛⠛⢻⢸⣿⣿⣿⣿⣿⠭⣹⡗⠔⢿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣷⣶⣶⣶⣾⣷⣷⣾⣶⣶⣷⣶⣶⣶⣷⣶⣶⣿⣶⣾⣶⣶⣷⣶⣾⢸⣿⣿⣿⣿⣿⡛⢺⣏⠉⣽ ⣿⣭⣭⢨⣭⡅⣭⣭⢨⣭⣭⣭⡅⣭⣭⢨⣭⡅⣭⣭⢨⣭⣭⣭⡅⡭⠭⢨⠭⡅⠭⢭⡭⠭⢨⠭⠅⡭⢭⢨⠭⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣼⣿⣿⣿⣿⣿⠀⢸⡟⣍⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⢿⣿⡿⡇⣿⢿⢸⠿⡇⡿⢿⢸⢿⣿⡿⡇⡇⢸⠘⡀⡇⢀⢾⡇⢸⢸⠀⡇⣇⢸⠸⡠⣿⣿⣿⣑⣉⣉⣀⣏⣉⣩⡈⣽⣉⣉⣍⣁⣉⣽⣏⣽⣃⣁⣊⣙⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣗⠤⢿ ⣿⡗⡲⢸⢒⠇⣗⢺⠐⠅⣿⠪⠂⡇⠱⢸⠈⠆⠎⣸⠐⠕⣿⠈⠂⡇⢸⢨⠪⡇⠕⢽⡏⢺⢸⠀⡇⡗⢽⠨⠪⣿⣿⡟⡟⣋⠛⢛⣿⠛⢛⠋⠛⠙⠛⢻⠻⢛⠛⡟⡏⠋⡍⡋⠋⣿⣿⣿⣿⣿⣿⣿⣿⠐⢹⡯⢀⣿ ⣿⣧⣮⢸⣴⡅⣷⣾⢠⣥⣿⣤⡄⣯⣭⢸⣥⡅⣭⣽⢨⣬⣿⣭⡅⡇⢘⠰⡀⡇⢀⢸⡇⢈⢸⠀⡇⣇⢸⠰⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⡯⠄⣻ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣇⣰⢸⣀⡇⣀⣾⣇⣰⢸⣄⡆⣇⣸⢸⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣿ ⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠔⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿ ⣿⣭⣭⢩⣭⡍⣭⣭⢩⣭⣭⣭⡍⣭⣭⢩⣭⡍⣭⣭⢩⣭⣭⣭⡍⣭⣭⢩⣭⡍⣭⣭⣭⣭⢩⣭⡍⣭⣭⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⡧⡤⣿ ⣿⡏⠉⢸⠍⡇⡯⢹⠀⠁⣿⠈⠁⡏⠩⢸⠍⡇⡭⢸⠀⠁⣿⠈⠁⡯⠩⢨⠅⡇⠈⢸⡇⠁⢸⠍⠇⡯⢹⢨⠅⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⡿⠟⡟⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠲⣿ ⣿⡇⠀⢸⠕⡇⡇⢺⠀⣀⣿⠠⠀⡇⢈⢸⠀⡇⡣⣺⠀⠀⣿⡠⠀⡇⢈⢘⠐⡇⠊⢸⡗⣁⢸⡫⡃⡿⢽⢸⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣐⣻ ⣿⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⢸⠿⡇⡿⢿⠸⠿⣿⠿⠇⡿⠿⢸⡿⠇⢿⢿⠸⠿⣿⠿⠇⣿⠿⠸⡿⡇⠿⢿⡿⠿⢸⠿⡇⡿⢿⢸⠿⣿⣿⣿⢿⣿⣿⢿⣿⠿⠿⠿⢿⣿⣿⠿⣿⣿⢿⢿⠿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣤⢸⣬⡅⣧⣽⢨⣂⣿⣄⡄⣇⣭⢸⣬⡅⣕⣽⢠⣤⣿⣤⡅⣧⣭⢨⣬⡇⣥⣽⣧⣢⢸⣴⡅⣗⣼⢸⣬⣿⣿⣿⣦⣤⣼⣤⣼⣥⣤⣬⣬⣿⣴⣧⣤⣾⣤⣴⣤⣶⣬⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⡃⣛⣛⢘⣛⡃⣛⣛⣛⣛⢘⣛⡃⣛⣛⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⠀⡆⡇⢸⢸⠀⣿⣿⣿⢛⠛⠛⠙⡟⠛⢟⠛⣻⡻⠛⡛⠛⠻⣻⡟⣻⠛⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⣭⢸⢭⡇⣯⣽⠈⢭⣿⢉⡁⡏⣩⢸⢉⡇⣍⣹⠈⣉⣿⢉⡁⡏⣩⢸⣉⡇⢍⣹⡏⣉⢰⠀⡇⡆⢸⢐⢐⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⡷⣿⠿⠿⠿⠿⠿⡿⡿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣗⢕⢸⠨⡂⡯⢽⢐⠅⣿⣂⡂⡇⢔⢸⢄⡂⣂⣸⢐⡂⣿⣀⡂⣇⣒⢰⡑⡇⡆⣺⡗⣒⢸⣀⡇⣗⣸⢰⣰⣿⣿⣿⣿⣿⣧⣶⣶⣦⣾⣷⣶⣷⣶⣶⣶⣼⣾⣶⣾⣼⣾⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⡀⡇⡇⢸⠰⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣀⣀⣠⣃⣨⣆⣞⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣭⣭⢨⣭⡅⣭⣭⢨⣭⣭⣭⡅⣭⣭⢨⣭⡅⣭⣭⢨⣭⣭⣭⡅⣭⣭⢨⣭⡅⣭⣭⣭⣭⢨⣭⡅⣭⣭⢨⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⢹⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⢿⠿⠿⢿⠿⢿⢿⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢻⡛⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠉⢸⠉⡃⣏⢽⠈⠉⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣮⣤⣦⣵⣤⣤⣤⣧⣦⣤⣤⣤⣤⣼⣤⣠⣼⣶⣧⣴⣤⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⢸⣶⡇⣿⣿⢰⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣏⠛⢉⡛⢉⡙⡻⢹⢙⠛⣟⠋⠛⠉⡍⠛⠛⣟⠫⢹⠍⠕⡉⠋⢹⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⢸⣿⡇⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⣶⢰⣶⡆⣶⣶⢰⣶⣶⣶⡆⣶⣶⢰⣶⡆⣶⣶⢰⣶⣶⣶⡆⣶⣶⢰⣶⡆⠒⢶⡖⢲⢰⠒⡆⡖⢲⢰⠲⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⢶⣶⣶⣶⣶⡶⣶⣶⣶⣶⠶⠶⠶⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⢸⠿⡇⡿⢿⠸⠛⣿⢛⠃⡟⠻⢸⠛⠇⠟⢻⠸⡛⣿⢛⠇⡟⠻⠸⠛⡇⡡⣺⡇⢸⢨⠁⡇⡭⣸⢈⢕⣿⣿⣿⣬⣤⣤⣤⣧⣤⣴⣤⣾⣴⣤⣦⣤⣴⣾⣧⣾⣥⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠉⢸⠉⡇⡏⢹⠀⡉⣿⠈⠁⡇⣉⢸⢛⠃⢋⢽⠀⡉⣿⢈⠁⡇⢉⢸⡫⡇⠈⢾⡇⢼⢸⠠⡇⡏⢸⠰⠱⣿⣿⣿⢈⣁⣈⣉⣇⣁⣩⣁⣉⣈⡉⣏⣈⣁⣉⢸⣁⣣⣶⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⢸⣶⡇⣷⣾⢰⣶⣿⣶⡆⣷⣾⢸⣷⡇⣷⣿⢰⣶⣿⣷⡆⣷⣶⢸⣶⡇⠀⢼⡇⠠⢸⠀⠄⡇⠨⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⣩⡿⡙⡟⡉⠭⠫⢽⢋⡋⡟⠍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣬⣥⣦⣱⣯⣥⣮⣌⣼⣥⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠛⡟⢻⣿⠛⣝⢛⠹⢿⠿⢿⢟⠛⡿⠿⠿⢿⠿⠿⣿⠋⢿⢿⠿⠻⠹⢿⠿⡿⢿⡿⢿⠿⠟⠻⠿⡿⠏⡿⢻⠹⠿⠿⠛⣿⠿⡿⠿⢿⣿⡿⢿⠿⢿⣿⡿⣿⢿⣿⢿⡿⢿⢿⡿⢿⢿⣿⣿⡿⡿⢿⣿⣿⣿ ⣿⣿⣿⣧⣥⣥⣼⣽⣿⣿⣼⣼⣼⣤⣼⣮⣤⣧⣦⣥⣬⣄⣥⣾⣤⣬⣼⣼⣬⣼⣴⣤⣦⣿⣧⣧⣬⣤⣤⣤⣧⣥⣿⣼⣼⣤⣤⣤⣿⣦⣿⣧⣟⣿⣯⣽⣬⣿⣥⣿⣯⣵⣥⣽⣭⣼⣾⣿⣭⣯⣿⣿⣴⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣝⢟⣿⠛⣟⣛⣿⣻⣿⣫⢛⢻⣻⣻⡛⣿⣿⠻⣻⣟⣻⣟⣿⣟⣻⡟⣛⣿⣿⣿⣟⣿⣟⣯⣿⣿⣻⣿⣻⣟⡻⣗⣿⣽⣿⡏⣟⣟⣟⡻⠿⣿⣟⣿⣻⣻⠟⡿⣫⣿⣛⣻⡿⣿⣟⣯⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣾⣷⣶⣷⣿⣴⣶⣾⣿⣿⣬⣼⣷⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣶⣷⣾⣷⣾⣿⣿⣷⣶⣿⣿⣿⣾⣾⢶⣷⣿⣿⣿⣿⣿⣿⣷⣿⣷⣷⣿⣾⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢯⠍⢿⢻⢿⡯⣿⡭⣿⣭⣿⢿⣽⡯⢽⣯⣿⡍⡟⣻⡯⢽⣿⣧⡗⢟⣍⣹⣿⡯⢽⢯⠹⠃⠽⡟⣻⠯⣹⣿⢿⡭⠛⣿⡩⢿⢺⡟⡭⣏⢹⢿⡿⡏⣹⣿⠛⢻⠍⡍⣿⢋⢩⣯⡟⣙⠽⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣷⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣸⣿⣗⣖⣿⣺⣐⣗⣿⣝⣒⣾⣽⣽⣮⣯⣧⣹⣿⣗⣿⣿⣯⣸⣉⣗⣺⣳⣷⣿⣾⣒⣵⣾⣗⣢⣶⣾⢿⣇⣺⣛⣠⣏⣿⣑⣸⣏⣇⣹⣜⣇⣛⣿⣺⣒⣽⣷⣾⣼⣽⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠟⠿⠿⠟⢿⠟⠟⢿⠿⠟⠿⠻⠿⠋⠹⠿⢿⠉⢻⠹⠻⠉⢻⡿⠿⠹⢻⠹⢿⠿⢿⠙⠿⠹⡿⠻⠟⣿⠿⠟⢹⡏⠻⢿⢿⠉⠻⠋⢹⠟⠿⠻⣿⢿⠻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣬⣤⣤⣤⣧⣤⣴⣬⣤⣴⣤⣥⣤⣤⣼⣤⣼⣠⣿⣤⣼⣄⣀⣤⣼⣧⣤⣤⣤⣤⣽⣦⣼⣤⣽⣤⣤⣤⣼⣿⣬⣤⣼⣧⣥⣬⣼⣤⣤⣥⣼⣼⣄⣀⣿⣬⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠋⡏⠛⢉⠛⠙⠘⠛⠛⠙⠉⠛⢹⡟⡙⡟⣻⢋⢛⢰⡏⡁⡛⠟⢹⡟⠙⡋⠟⠹⠋⡋⡛⢻⡇⡙⠋⠛⠛⡙⠋⢹⡇⢛⢹⠛⢻⢻⢐⢐⠘⣙⠘⠙⡟⡙⢙⣟⢹⢋⢻⡟⢙⢻⠋⠛⠙⠉⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⢷⣶⣾⣤⡾⢾⣶⣶⣾⠶⡷⣾⡷⣶⣷⣿⣶⡾⣾⢷⣶⣷⣷⣾⣷⣶⣶⣶⣾⣶⣷⣶⣾⣷⣶⣶⣾⣶⣷⣤⣼⣷⣾⣿⣶⣶⣾⣾⣾⣶⣶⣶⣶⣷⣷⣶⣿⣶⣶⣾⢷⣾⣾⣶⣶⣶⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠠⢠⢹⠁⢹⡇⠈⠈⠀⢈⠀⡇⠀⡇⠁⠩⠘⢿⡇⠿⡈⠘⠁⡌⠁⢸⡏⠈⣿⣿⠻⢹⡻⡏⣡⣿⡯⣻⢷⣿⣿⣭⢩⣹⠪⣿⡟⣻⣾⣿⠁⠉⠨⠈⠹⢸⢡⡅⡇⠌⠠⢸⠡⠁⡌⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢿⡿⣿⣿⡟⡿⢻⡟⡿⢿⡿⣿⠟⣿⠿⡿⣿⣿⢿⣿⢿⡿⢶⡾⡿⠿⢿⡛⢿⣿⣿⠿⢻⠿⡿⢿⣿⠿⠿⡿⢿⢿⣿⠿⠻⣿⢿⠿⣿⠿⣿⣿⣿⣿⣿⢿⣷⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣆⣘⣠⣃⣇⣐⣸⣇⣄⣸⣀⣀⣂⣿⣐⣘⣸⣇⣀⣧⣒⣐⣸⣰⣀⣂⣾⣀⣂⣄⣀⣘⣠⣒⣄⣆⣿⣰⣀⣀⣂⣁⣿⣘⣰⣀⣁⣄⣿⣷⣋⣸⣖⣧⣗⣡⣎⣟⣻⣻⣽⣻⣹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣟⣿⣿⢿⠿⡿⡿⣿⣿⣿⢟⣿⢿⠿⡿⣿⢿⠿⡿⢟⣿⣿⣟⢿⣽⡟⡿⡿⡿⣻⢿⣫⣿⢿⣹⠿⡿⣿⣟⣿⢿⡿⡿⣿⢿⠿⡿⢿⢿⡿⣿⣭⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣮⣼⣿⣬⣿⣿⣮⣾⣯⣿⣺⣿⣭⣧⣿⣿⣯⣿⣿⣬⣯⣵⣭⣯⣿⣯⣿⣿⣯⣭⣿⣯⣽⣮⣷⣯⣽⣽⣿⣇⣺⣿⣽⣿⣿⣭⣿⣭⣦⣭⣼⣿⣦⣿⣯⣯⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠩⠛⣝⢫⠋⢙⢩⢫⢹⠊⡝⠫⢹⡏⡅⡝⠯⢩⢹⣏⢽⢈⠛⡝⢋⡍⡽⡏⡝⠝⢋⡋⢉⢹⡏⠀⡏⡟⢫⡏⡍⡏⠫⢫⢹⠘⡝⡏⡝⡩⣿⠩⠋⡙⡍⡟⠛⢉⠙⠉⢸⠉⣏⡙⠫⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠶⡶⣶⣶⣶⣾⣴⣾⣶⣶⣷⡤⣼⣷⣶⣷⣷⣾⣾⠷⣾⣾⣶⣶⣾⣷⣾⣷⣶⣶⣾⣷⡾⣾⣿⣷⣷⣶⣶⡶⡶⢶⡶⣾⣾⣶⣶⡷⣷⣶⣿⣶⡶⠷⣶⣷⣶⣾⣾⣶⣾⣷⡿⣷⣶⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⢎⠑⠩⠐⠰⣏⠀⠅⠂⠆⡇⡌⡘⠀⠁⠎⠂⣶⣿⡓⠨⠐⠕⡉⠉⢰⢰⠁⠄⡆⠆⡱⢈⢰⢹⡏⠈⡀⡇⢸⡇⡃⢨⠀⡃⠆⣿⠰⠱⢹⡇⡆⠸⢸⠰⡆⠇⠇⠑⠁⠎⡏⠎⢠⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⠿⣿⠿⠟⢿⡿⣿⠟⠻⡿⠿⢿⠿⠛⡿⢿⠿⢿⠿⡿⠿⢿⢻⠿⣿⢟⠿⡿⢷⠿⣿⡿⢿⠿⡿⠿⢿⡿⠿⢿⠿⡿⢿⠻⢿⡟⡻⢛⣻⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣸⣺⣸⣇⣃⣇⣀⣸⣇⣇⣃⣸⣠⣀⣀⣇⣀⠀⢻⣰⣉⣸⣘⣀⣃⣿⡸⣊⣇⣐⣀⣸⡇⣠⣀⣀⣇⣁⠈⢀⣮⣁⡇⣪⣸⣸⣗⣢⣒⣸⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠿⣿⢿⣿⠿⡻⠿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⡟⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡟⣿⣿⣿⡿⣿⢻⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣇⣂⣅⣨⣻⣶⣿⣸⣰⣸⣀⣼⣜⣉⣇⣄⣂⣘⡀⣂⣽⣰⣸⣀⣇⣸⣇⣂⣆⣁⣸⣰⣀⣀⣆⣂⣰⣁⣨⣇⣂⣅⣨⣐⣇⣐⣈⣀⣕⣂⣷⣀⣐⣸⣃⣸⣐⣀⣂⡃⣀⣐⣗⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⢙⠿⢿⠿⠿⢿⢿⠿⠿⠻⣿⠿⠿⠟⠿⠿⣿⠿⠟⢹⣟⢛⣿⣛⣿⢻⣿⣿⣿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣬⣼⣤⣴⣬⣬⣼⣤⣤⣧⣤⣿⣼⣤⣤⣥⣤⣿⣬⣤⣼⣯⣬⣽⣭⣭⣭⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ䷩ 𝚕𝚒𝚗𝚎 1756 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/07/fictional-epo-gap/#comments Gemini version at gemini://gemini.techrights.org/2022/01/07/fictional-epo-gap/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Fictional_Gaps_and_an_Attack_on_Workers⠀✐ Posted in Europe, Patents at 11:58 am by Dr. Roy Schestowitz Video_download_link | md5sum a5e2aade7a2a72ff78d2c9de88d34275 The EPO’s Fake Gap Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/epo-finances-fake-gap.webm Summary: Benoît_Battistelli‘s EPO, which is now run by his longtime sidekick António_Campinos, is racing to the bottom of patent quality and patent examination; the ramifications are profound, even if the media is mostly silent on this issue THE video above, which is the first we make with metadata in it (experimental code), was improperly recorded so there’s background noise. Nevertheless, it looks back at the parts published here throughout the week, dealing with the “race to the bottom” seen at the EPO. The parts discussed are as follows: 1. The_EPO’s_Race_to_the_Bottom_—_Part_I_—_From_Bad_to_Worse 2. The_EPO’s_Race_to_the_Bottom_—_Part_II_—_“Playing_People_Off_Against_Each Other_is_Not_the_Way_We_Want_to_Go_Forward!” 3. The_EPO’s_Race_to_the_Bottom_—_Part_III_—_“The_King_is_Naked”_(a_Fake Financial_Shortage_and_‘Missing’_—_or_Plundered_—_Billions) 4. The_EPO’s_Race_to_the_Bottom_—_Part_IV_—_New_Career_System_(NCS)_and_New Pension_System_(NPS) 5. The_EPO’s_Race_to_the_Bottom_—_Part_V_—_An_Assault_on_Pensioners As noted near the start of the video, there’s some experimental code involved (changelog_here), so it’s not exactly shocking that the quality was subpar. Over the coming year we’ll hopefully make further improvements to the workflow and provide more material per time unit. At the EPO, the number of workers is decreasing, so the load each person deals with is increasing. It’s hardly surprising that quality_goes_down_the_drain. █ ䷩ 𝚕𝚒𝚗𝚎 1812 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/07/irc-log-060122/#comments Gemini version at gemini://gemini.techrights.org/2022/01/07/irc-log-060122/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ IRC_Proceedings:_Thursday,_January_06,_2022⠀✐ Posted in IRC_Logs at 2:47 am by Needs Sunlight Also available via the Gemini protocol at: * gemini://gemini.techrights.org/irc-gmi/irc-log-techrights-060122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-060122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-social-060122.gmi * gemini://gemini.techrights.org/irc-gmi/irc-log-techbytes-060122.gmi Over HTTP: 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #techrights_log_as_HTML5 #boycottnovell_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇H 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇HTML5_logs⦈_ #boycottnovell-social_log_as_HTML5 #techbytes_log_as_HTML5 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #techrights_log_as_text #boycottnovell_log_as_text 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇t 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇text_logs⦈_ #boycottnovell-social_log_as_text #techbytes_log_as_text Enter_the_IRC_channels_now =============================================================================== § IPFS Mirrors⠀➾ CID Description Object type IRC log for  QmfFyx3vwxbqSY1amGkY933nxsSQnUfgGvaJkTnAhYNVrb #boycottnovell 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell  QmTbRY3mN1bMk7JhVqLGhjY6nZJxu54XyhvZTKqizmJMNS (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for #boycottnovell-  Qma127EEwNM9aYCtY1Fo3SEfScDg51wYE8ufdyx5yNxn2J social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #boycottnovell-  QmNueMQCUVjHNYmQfnA9vb8zpvg7FouuMZbQP3mq6XnvS1 social 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ (full IRC log as plain/ASCII text) IRC log for  QmZHptF6kKVavS5rS4L3x6CziYTZWehtvPMZYaYXPczzXa #techbytes 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techbytes  QmSgXPNax7eDXeCEJUavyGkMp21BEAcg3dAVVDp67pfvPZ (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) IRC log for  QmW8RgjWW7pmkf9r3XGrK2XTMK1KQkCYtwnho9uPsiHnmK #techrights 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇HTML5 logs⦈ (full IRC log as HTML) IRC log for #techrights  QmcQ5X4ySmmdAsJ534ezbATmjffAqLHqYnAdVAzmf5bG9A (full IRC log 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇text logs⦈ as plain/ASCII text) 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇IPFS logo⦈ § Bulletin for Yesterday⠀➾ Local_copy | CID (IPFS): QmfKHqGowjRxdQqskGCLaTJvfCGFi19QHkyd8kwa9PMJ21 ䷩ 𝚕𝚒𝚗𝚎 1939 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/07/techrights-videos-metadata/#comments Gemini version at gemini://gemini.techrights.org/2022/01/07/techrights-videos-metadata/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Techrights_Updates:_Metadata_in_Videos_and_More⠀✐ Posted in Site_News at 2:05 pm by Dr. Roy Schestowitz Video_download_link | md5sum 0bce67674b493eea072ca1e1491c4125 Updates on Gemini, Git, and Videos Creative Commons Attribution-No Derivative Works 4.0 http://techrights.org/videos/gemini-and-video-update.webm Summary: We take stock of some recent changes and developments, which are partly bad news and partly good news THE public archive of the Gemini mailing list has been down for a number of weeks already. It’s a darn shame, but there’s a plan to correct the issue some time soon. In the words of the official site: § Welcome back to emptiness; from emptiness⠀➾ The hard-drive is unwell, perhaps permanently so. All services are gone. Some will come back in time. If you appreciated one of the services and would like it back, or anything else, contact me: mail: fox at orbitalfox.eu tox: 4E7B071824885E8B4B82D6570292B42F997BAB2FD742FB1589F3084FB377B160E01B9C6BF9D0 The official site of Gemini says at the very top: § Announcement⠀➾ The mailing list is currently down due to a hardware failure. It will reappear in some form or another as soon as possible. Watch this space. Undeterred by this setback, the Gemini space (or Geminispace) continues to expand. According_to_Lupa: There are 1927 capsules. We successfully connected recently to 1567 of them. It seems safe to predict 2,000 capsules this month or next month. The video above is commentary about the state of Gemini and the new metadata added to video files generated with our scripts (changes are visible in Git, which we only make available over gemini://). Gemini Protocol is quickly gaining popularity among Free software folks; we hope to see 5,000 capsules by the end of this year. █ ䷩ 𝚕𝚒𝚗𝚎 2023 ╒═══════════════════ 𝐀𝐑𝐓𝐈𝐂𝐋𝐄 ═════════════════════════════════════════════════╕ (ℹ) Images, hyperlinks and comments at http://techrights.org/2022/01/07/the-gap/#comments Gemini version at gemini://gemini.techrights.org/2022/01/07/the-gap/ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ [Meme]_Diferençampinos⠀✐ Posted in Deception, Europe, Finance, Patents at 7:10 am by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴_🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽_⦇We'll_tell_them_there's_a_'gap'_and_rob_the_pensioners⦈_ Summary: Today we concluded a series about the EPO‘s attack on pensioners, based on a fictional_"gap" touted by António_Campinos Series index: 1. The_EPO’s_Race_to_the_Bottom_—_Part_I_—_From_Bad_to_Worse 2. The_EPO’s_Race_to_the_Bottom_—_Part_II_—_“Playing_People_Off_Against_Each Other_is_Not_the_Way_We_Want_to_Go_Forward!” 3. The_EPO’s_Race_to_the_Bottom_—_Part_III_—_“The_King_is_Naked”_(a_Fake Financial_Shortage_and_‘Missing’_—_or_Plundered_—_Billions) 4. The_EPO’s_Race_to_the_Bottom_—_Part_IV_—_New_Career_System_(NCS)_and_New Pension_System_(NPS) 5. The_EPO’s_Race_to_the_Bottom_—_Part_V_—_An_Assault_on_Pensioners ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⢠⣶⣿⣿⡟⢻⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠸⣿⠿⠁⠀⢹⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣽⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣽⡛⠿⣿⣿⣿⣿⣠⠈⠁⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⡄⢠⡀⠀⠀⠀⠀⠀⢻⣿⠸⣿⣿⡟⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⢾⣗⣌⣠⣬⣿⣿⣿⡿⠺⣿⣿⡿⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣜⣿⣷⣾⣿⣧⠀⠀⠀⠀⠈⣿⠐⣿⠻⡇⢸⣿⣿⣿⣉⡈⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣦⣀⡉⠈⠁⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠄⠀⠀⠀⠘⡃⠀⣿⡦⠀⠘⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⠠⠱⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⡿⠟⠒⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢦⣤⣴⣧⣤⡼⠄⠀⠀⠀⠀⠀⠀⠹⠉⠄⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠳⠄⠀⣀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⠷⢤⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⠤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⠀⢠⣤⣄⣥⠄⠀⠀⠀ ⠀⠀⠛⢻⣿⣿⣿⠿⠿⠿⢿⡄⢀⡀⠑⠒⠋⠀⠸⣶⣬⣴⣦⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣽⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⢻⡏⠀⠀⠀⢂⡾⠧⠅⡻⣦⣀⣀⣴⣾⣟⣻⡿⡿⡿⣧⡀⠀⢀⡀⣙⡋⠁⢸⡧⠀⠀⠀⠀⠀⣸⣧⢹⣿⣿⣿⠀⠉⣻⣿⣿⣿⣿⣾⡿⣿⡏⠉⡤⠄⠀⠈⠀⠀⠀⡞⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠠⢹⣿⣿⣿⣿⣿⡿⠋⠈⡇⠀⠬⠷⡀⠈⠱⣦⡟⣼⢸⡆⠀⠶⠂⠀⣼⣿⣿⢸⣿⣿⣷⣦⠤⢛⣻⣿⡟⣿⢇⣆⣹⣿⣶⠀⠀⢰⠖⠀⠀⠀⠠⢾⠟⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⠿⠟⠛⠛⠛⠿⣶⣾⣿⣿⣤⣌⣻⣿⠿⠋⢀⡘⠁⢀⠀⠀⠈⢹⡄⠀⠀⢣⢹⣿⡇⠀⠚⡆⣸⣿⢻⡿⡜⢿⣿⣿⠋⢠⣿⣿⣿⣱⢧⣿⣿⣿⣿⣶⡠⣄⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣭⢍⣭⣭⢭⣭⣤⡄⣤⠄⢤⡤⢤⣶⢤⡤⣬⡤⣤⣬⡌⢠⡤⠀⠀⡥⣥⠥⣤⢥⡤⣬⢽⡯⣽⢛⣿⢿⣯⢥⡬⣭⡥⣭⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⢄⡸⠏⠰⠟⠹⠇⠿⠽⢼⠹⠯⠿⡘⠁⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢤⡄⢤⢤⡤⣄⠐⢢⡤⣤⢀⡤⣯⢨⡥⣤⢻⢠⣤⣤⢤⡭⣥⢤⡤⣬⠝⢠⡤⣄⣤⢤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⢿⡘⣸⡿⣯⢿⣅⡿⣸⣯⡿⢈⢀⣿⢀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⠛⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⠿⠿⠃⠀⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠜⠈⠀⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⢟⣝⣿⡛⠿⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⠀ ⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⡄⢠⡀⠀⠀⠀⠀⠀⢸⣿⠠⣿⣿⡟⣻⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⡿⠻⣷⣿⡞⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣘⣻⣿⣼⣿⣦⠀⠀⠀⠀⠈⣿⠀⣿⠿⠇⢸⣿⣿⣟⣟⠈⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣷⢀⡉⠈⠁⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠄⠀⠀⠀⠰⢹⠀⣿⣶⠀⠈⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠠⠴⠟⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⢿⠳⠂⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢦⣤⣤⣦⣤⡼⠄⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠳⠆⠀⣀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢙⡿⠥⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⢴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⠀⠠⣤⣤⣱⠆⠀⠀⠀ ⠀⠀⠛⢻⣿⣿⣿⡿⠿⠿⢿⡆⠀⡀⠑⠒⠋⠀⠘⣶⣬⣴⣤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⢻⡏⠀⠀⠀⠂⡾⠧⠀⠻⣦⣀⢀⣴⣾⣟⣻⡿⡿⡿⣧⡀⠀⢀⡈⢉⡟⠁⢼⡷⠀⠀⠀⠀⠀⣠⣟⢹⣿⣿⣿⡄⠉⣻⣿⣿⣿⣿⣾⡿⢿⣏⠉⣤⠤⠀⠀⠀⠀⠀⡞⠁⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣤⣾⡀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⡿⠋⠀⠇⠀⠬⠽⡀⠰⠡⡄⡿⢺⣿⡇⠀⠴⠂⠀⣸⣿⣿⢸⣿⣿⣷⣶⡤⢙⢻⣿⡿⣽⢏⣤⣸⣿⣶⡀⠀⢀⡖⠀⠀⠀⠀⢾⠝⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⠿⠿⠿⠛⠛⠛⠿⣶⣶⣿⣿⣤⣌⣻⣿⠧⠋⢀⡘⠁⠀⠀⠀⠀⠙⣆⠀⠀⢧⣸⡿⡇⠀⠘⡆⣰⣿⢟⣻⡜⢿⣿⣿⠋⢠⣾⣿⣿⢡⡏⣿⠿⢿⣿⣶⡄⣄⠈⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣭⢍⣭⣭⢭⣭⣤⡄⣤⠄⢤⡤⠤⣶⢤⡤⣬⡤⣤⣬⡌⢣⡤⠀⠀⡤⣭⠭⣤⢭⡤⣬⢽⡯⣽⢛⣿⢿⣿⢤⡤⣭⡥⣬⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠤⠸⠧⠄⠄⠸⠏⠰⠟⠹⠇⠿⠽⢼⠹⠯⠿⡘⠁⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣨⡒⢤⡄⢤⢤⡤⣄⠀⢢⡤⣤⢀⡤⣮⢨⡥⣤⢻⢠⣤⣤⢤⡭⣥⢤⡤⣬⠿⢠⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢈⢀⣿⢀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⡿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⠿⠉⠀⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠈⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⠟⣍⣿⡛⠿⣿⣿⣿⣿⣀⠁⠀⠀⠀⠀⠀⠀ ⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⡄⢠⡀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡿⢿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⣀⢠⣀⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⡿⠾⣿⣿⣿⡂⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣘⣻⣯⣼⣿⣦⠀⠀⠀⠀⠈⣿⠀⣿⠿⡇⢸⣿⣿⣟⣉⡁⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣾⣿⣿⣟⡛⡿⣿⣿⡝⠃⢿⣿⣷⣄⢈⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠄⠀⠀⠀⠨⢹⠀⣿⣾⡃⠘⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠲⢓⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⠟⠛⠂⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⢦⣤⣤⣦⣤⡼⠄⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠳⠆⠀⣀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⡿⠥⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⠀⠠⣤⣄⣡⠦⠄⠀⠀ ⠀⠀⠛⢻⣿⣿⣿⡿⠿⠿⢿⡆⠀⡀⠑⠒⠋⠀⠘⣶⣬⣴⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⢻⡏⠀⠀⠀⢊⡾⠧⠀⢻⢦⡀⢀⣴⣾⣟⣻⡯⡿⡿⣧⡀⠀⢀⡈⢙⡟⠁⢼⡷⠀⠀⠀⠀⠀⣠⣟⢹⣿⣿⣿⡄⠉⣻⣿⣿⣿⣿⣾⡿⢿⡏⠉⣠⡄⠀⠀⠀⠀⠀⡞⠁⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣤⣤⣾⡀⠀⠀⠀⠈⠀⠀⢠⢸⣾⣿⣿⣿⣿⡿⠋⠈⠇⠀⠬⠽⡀⠐⠀⡔⡟⢺⣽⡇⠀⠴⠂⠀⣸⣿⣿⢸⣿⣿⣷⣶⡤⢙⢻⣿⡿⣽⢏⣄⣸⣿⣶⡀⠀⢀⡖⠀⠀⠀⠀⢾⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⠿⠿⠿⠛⠛⠛⠿⣶⣶⣿⣿⣤⣌⣻⣿⠧⠋⢀⣘⠁⠀⠀⠀⠀⢙⣆⠀⠀⢣⢸⡿⡇⠀⠘⡆⣰⣿⢯⣯⡜⢿⣿⣿⠋⢠⣾⣿⣿⢡⡏⣿⡿⢿⣿⣶⡤⣄⠈⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣭⢍⣭⣭⢭⣭⣤⡄⣤⠄⢤⡤⠤⣴⢤⡤⣬⡤⣤⣬⡌⢣⡤⠀⠀⡥⣭⠭⣤⢭⡤⣬⢽⡯⣽⢛⣿⢿⣿⢤⡤⣭⡥⣬⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠤⠸⠧⠄⠄⠸⠏⠰⠟⠹⠇⠿⠽⢼⠹⠯⠿⡘⠁⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢦⡄⢤⢤⡤⣄⠀⢢⡤⣤⢀⡤⣮⢨⡤⣤⢻⢠⣤⣤⢤⡭⣥⢤⡤⣬⠕⢠⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢈⢀⣿⢀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣽⣿⣿⡿⠿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⢿⠋⠀⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠋⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠡⠀⠀⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣑⠈⡀⠀⠀⠀⠀⠀ ⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⡀⢀⡀⠀⠀⠀⠀⠀⢸⣿⠄⣿⣿⡿⢻⣿⣿⣿⣿⠿⠧⠀⠀⠀⠀⠀⠀⣀⣀⣀⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣾⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⠿⣿⣿⣾⣃⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣨⣻⣯⣼⣿⣦⠀⠀⠀⠀⠈⢻⠀⣿⡿⡏⢸⣿⣿⣿⡻⠁⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣾⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣷⣄⠈⠉⠁⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⣻⠀⢿⣷⡄⠀⣻⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠢⠾⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⡟⠛⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢦⣄⣠⣧⣤⣼⠄⠀⠀⠀⠀⠀⠀⠘⠀⠄⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠖⠀⣀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢙⡿⠭⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⢴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠿⠋⠉⠉⠀⠀⠀⠠⣤⣠⣁⣤⠄⠀⠀ ⠀⠀⠛⢻⣿⣿⣿⣿⣿⠿⢿⡇⠀⡀⠑⠒⠊⠀⠘⣶⣬⣖⣤⣄⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠚⠻⡏⠀⠀⠀⠀⡼⠧⠀⠷⢦⣀⢀⣰⣾⣟⣻⡿⣿⣿⢧⡀⠀⠀⣀⣈⣟⠉⣍⣿⠀⠀⠀⠀⠀⢠⣿⣼⣿⣿⣿⡄⠉⣻⣿⣿⣿⣿⣾⡿⢿⣏⠋⣠⡄⠀⠀⠀⠀⠀⡶⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣤⣤⣾⡁⠀⠀⠀⠈⠠⠀⢠⢸⣾⣿⣿⣿⣿⡿⠋⠀⠇⠀⠬⠽⠀⠈⠁⠴⠹⢪⣯⡇⠀⠰⠆⠀⣰⣿⣯⣏⣿⣿⣽⣶⡤⠙⢻⣿⡿⣹⡟⣄⡸⣿⣶⡀⠀⠀⡖⠀⠀⠀⠀⣼⡿⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⠿⠿⠿⠟⠛⠻⠿⣶⣶⣿⣿⣤⣌⣻⣿⠿⠋⢀⢘⠁⠀⠀⠀⠀⠙⣆⠀⠀⢦⡈⡟⡿⠀⠸⢴⢠⣿⡟⣏⣇⢻⣿⣿⡟⢁⣼⣿⣿⢇⡟⣾⣿⠿⣿⣵⡄⣀⡈⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣭⢍⣭⣭⢭⣭⣤⡄⣤⠄⢤⡤⠠⣴⢤⡤⣬⡤⣤⣤⡄⢣⡤⠀⠀⡬⣬⠭⣤⢭⡤⣤⢿⡯⣴⢚⣿⢿⣿⢤⡤⣭⡥⣬⠭⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⡀⡸⠏⠰⠟⠹⠇⠿⠽⢼⡹⠯⠿⢸⠃⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢦⡄⢤⢤⡤⣄⠀⢢⡤⣤⢀⡤⣮⢠⡤⣤⢺⢠⣤⣤⢤⡬⣭⢥⡤⣬⠏⢡⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⡈⣸⡿⣯⢿⣅⡿⣸⣯⡿⢈⢀⣿⢀⣿⢩⣏⣸⣟⡇⠀⣼⡋⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣇⠀⠀⠀⠀⠀⣲⣾⣿⣯⢻⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⢿⡿⠋⠀⢀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⠟⣝⣿⡛⠿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣿⣿⠻⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣬⣿⣿⣿⣿⠿⣿⣿⣶⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡨⣻⣦⣼⣿⣦⠀⠀⠀⠀⠀⢹⡆⢸⡿⢿⠀⣿⣿⣿⣩⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣷⡄⢈⠉⠁⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠏⠀⢸⣷⡀⠀⢿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠒⠲⢾⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⠿⠛⠓⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢦⣅⣠⣿⣀⣼⠄⠀⠀⠀⠀⠀⠀⠈⠝⠂⠀⠈⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣑⢣⣿⡿⠉⠉⠻⠖⠀⣀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢙⡿⠍⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣯⣷⣯⡗⠾⠿⠋⠉⠉⠀⠀⠀⠠⣤⣤⡁⡠⠀⠀⠀ ⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠲⠚⠁⠘⣶⣄⣒⣤⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⠻⡏⠀⠀⠀⠀⣼⣧⠀⠳⣦⡀⢀⣠⣶⣟⣻⡿⡿⣿⢷⡀⠀⠀⣀⠁⣛⠋⠁⣿⠀⠀⠀⠀⠀⢀⣿⡟⣿⣿⣿⣆⠉⢻⣿⣿⣿⣿⣾⡿⢿⣏⠋⢀⣄⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣄⣾⡁⠀⠀⠀⠀⠠⠀⠀⢵⣺⣿⣿⣿⣿⡿⠋⠀⠇⠀⠨⠽⠀⠀⠉⢂⡽⢦⣏⣷⠀⠠⠦⠀⢠⣿⣯⡇⣿⣿⣭⣦⣤⠝⠛⣿⣿⢫⡿⣠⣀⣿⣷⡀⠀⠀⡔⠀⠀⠀⠀⣼⡿⠓⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⠿⠿⠟⠓⠺⠷⣶⣦⣯⣿⣤⣈⣻⣿⠿⠋⠀⣐⠁⠀⠀⠀⠀⠉⣆⠀⠀⠐⡈⣿⣿⠀⠈⢴⢀⣿⡿⣏⢇⢻⣿⣿⡿⠁⣴⣿⣿⡏⡾⣸⡿⡿⣿⣭⣔⣀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣭⢍⣭⣭⢭⣭⣤⡄⣤⠄⢤⡤⢠⣤⢤⡤⣬⡤⣤⣤⡄⢣⡤⠀⠀⡬⣬⠭⣤⢭⡬⣤⢽⡧⣴⢒⣿⢿⣿⢥⡤⣭⡴⣬⠭⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠤⠸⠇⠄⠀⠸⠏⠰⠟⠹⠇⠿⠹⠼⡹⠯⠿⢸⠃⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢦⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣼⢡⡤⣬⢺⣧⣤⣤⢤⡤⣭⢥⡤⣬⠏⢠⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⡠⣸⡿⣯⢿⣅⡿⣸⣯⡿⢈⢁⣿⠀⣿⢩⣏⣸⣟⡇⠀⣼⡋⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⣴⣾⣿⡿⠽⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⡿⠁⣀⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠠⠂⠀⠐⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⣿⣿⢏⣿⣿⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⢿⣶⣿⣷⠆⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣨⢿⣦⣼⣿⣦⠀⠀⠀⠀⠀⢹⡇⢸⡿⡿⠀⣿⣿⣿⢏⡁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣦⡩⡉⠉⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⡇⢸⣷⣎⠀⠛⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⢰⠮⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⠏⠓⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣤⢦⣍⣉⣽⣀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣑⢳⣿⡿⠉⠉⠻⠆⠀⣀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢙⡿⠍⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⢤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⠀⠠⣤⡤⣁⢠⡄⠀⠀ ⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠙⠶⠖⠃⠘⣦⣄⣒⣤⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠘⠻⡟⠀⠀⠀⠀⣼⣧⣀⠳⣦⡀⠀⣠⣾⣿⣛⡿⣿⣿⢷⡀⠀⠀⣀⡈⣻⠋⢉⣿⡆⠀⠀⠀⠀⢀⣼⡻⣿⣿⣿⣆⠉⢻⣿⣿⣿⣿⣾⡿⢿⣏⠋⢀⣀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣀⣼⡃⠀⠀⠀⠀⢀⠀⠀⠽⣾⢿⣿⣿⣿⡿⠋⠀⠇⠀⠨⠽⠄⠀⠋⢰⡸⢗⣷⢿⠀⠠⡤⠀⢀⣾⣿⡇⣿⣿⣯⣥⣤⠜⠿⣿⣿⢟⣿⢡⡀⢿⣷⡍⠀⠀⡤⠀⠀⠀⠈⣰⣾⠅⠐⠒⠑⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⠿⠿⠿⠗⠾⠷⣶⣦⣥⣿⣇⣈⣻⣿⠟⠟⠁⣐⠃⠀⠀⠀⠀⠀⣆⠀⠀⠘⡀⣿⢼⠀⠀⢥⠀⣾⣿⣻⣣⠻⣿⣿⡿⠃⣰⣿⣿⡟⣸⢳⣿⠿⣿⣯⣕⢀⠀⠁⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣭⢍⣭⣭⢭⣥⣤⡄⣤⠄⢤⡤⢠⣤⢤⡤⣬⡤⣤⣤⡅⢩⡤⠀⠀⡤⣬⠭⣥⢬⡤⣤⢽⡧⣴⢒⣷⢿⣿⢥⡤⣭⡴⣤⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠽⠼⣹⠯⠿⣸⠇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢦⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣴⢡⡤⣬⠲⣧⣤⣤⢤⡤⣬⢥⡤⣬⠛⢠⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⡠⣸⡿⣯⢿⣅⡿⣸⣯⡿⢀⣁⣿⠀⣿⢩⣏⣸⣟⣇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠀⠀⠀⠀⠀⣰⣿⣿⣟⠻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢾⠿⠟⠁⠀⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠁⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀ ⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⣿⣿⡇⣿⣿⣿⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣬⣿⣿⣿⣿⡷⣷⣶⣶⡂⠀⠀ ⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⢿⣦⣩⣿⣆⠀⠀⠀⠀⠀⢙⡇⢘⣿⢿⠀⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣄⡈⠉⠉⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡃⠘⣷⡬⠀⠘⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠐⢰⣾⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⡿⠗⠂⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⢤⣍⣉⣹⣅⣨⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣟⣭⣑⢃⣿⡿⠁⠉⠻⠗⠀⣀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⣻⡍⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣯⣷⣯⡷⠾⢟⡋⠉⠉⠀⠀⠀⠠⣤⣄⣁⢀⡀⠀⠀ ⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠾⠴⠃⠈⣦⣄⣂⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣷⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠻⡟⠁⠀⠀⠀⣼⣧⣀⡳⣦⣀⠀⣠⣶⣟⣛⣿⣿⣿⢷⡀⠀⠀⣀⠀⠸⠋⢉⢿⡇⠀⠀⠀⠀⠀⣸⣻⣿⣿⣿⣆⠉⠻⣿⣿⣿⣿⣾⣿⠟⣏⠋⢁⣀⠀⠐⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣀⣴⡃⠀⠀⠀⠈⠀⡀⠀⡌⣺⢿⣿⣿⣿⡿⠋⠀⠏⠀⠈⠽⠄⠀⠀⠀⢼⠇⣶⢹⠀⠀⡤⠄⠀⣾⣿⣭⣿⣿⣿⣥⣤⡘⠿⣿⣿⡟⣿⢃⡀⢿⣷⡌⠁⠀⣤⠀⠀⠀⠈⢠⢶⡢⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⠿⠿⠿⠿⠷⠶⠶⣶⣤⣤⣽⣇⣈⣛⣿⡏⠟⠁⣐⠃⠀⠀⠀⠀⠀⣆⠀⠀⠀⡀⣿⢸⠀⠀⢦⠀⣼⣿⢻⣹⠻⣿⣿⣿⠋⢠⣿⣿⡿⣸⢷⣿⣻⣿⣯⣅⢀⠀⠃⠀⠀⠀⠀⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣭⢍⣭⣭⢭⣥⣤⡄⣤⠄⢤⡤⢀⣤⣤⡤⣬⡤⣤⣤⡄⢨⡤⠀⠀⡤⣤⠭⣥⢽⡥⣤⢽⡧⣤⢒⣾⢿⣿⢥⡤⣬⡥⣤⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠤⠸⠧⠄⢀⠸⠏⠰⠟⠹⠇⠿⠹⠼⣹⠯⠿⣸⠇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢦⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣴⢣⡤⣤⠱⣦⣤⣤⢤⡴⣬⢭⡤⣼⠟⢠⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⡀⣸⡿⣯⢿⣅⡿⣸⣯⡿⠀⣁⣿⠀⣿⢩⣏⣸⣟⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡀⠀⠀⠀⠀⢠⣼⣿⣿⠙⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢾⣿⡿⠋⠀⢼⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠰⢿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣍⣿⡛⠿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⡏⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣾⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣷⢶⣦⣶⠂⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢘⡶⣤⣙⣷⣄⠀⠀⠀⠀⠀⠘⡷⠠⣿⢿⠇⢼⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠑⢾⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣇⢘⠋⠉⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠇⠀⣿⣦⠀⢘⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⢀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣯⣶⣄⢾⣿⣿⡿⠷⠗⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣡⢴⣍⡉⣩⣍⣩⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣑⢳⣿⡿⠁⠉⠻⠗⠂⣀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢻⣯⠉⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣯⣷⣯⡗⠾⠟⡋⠉⠉⠀⠀⠀⢀⣤⣂⠁⢀⣀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠯⠤⠇⠈⣦⣔⣂⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣷⣽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀ ⠀⠀⠀⠼⠿⡟⠉⠀⠀⠀⣼⣧⣈⡳⣶⣄⠀⣀⣶⣟⣻⣿⣿⢿⢷⡀⠀⠀⢀⡀⠸⡟⢉⢹⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣏⠉⠻⣿⣿⣿⣿⣾⣿⠿⣏⠟⠁⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣀⣴⡃⠀⠀⠀⠁⢀⡀⠀⡌⣨⣿⣿⣿⢿⣿⠏⠀⠏⠀⠈⣹⡄⠀⠈⠃⣘⠷⣲⣸⠀⠀⣤⠄⠀⣼⣿⣹⢹⣿⣿⣯⣄⡘⠿⢿⣿⡗⣿⢇⠄⢻⣧⡈⠁⠀⡠⠀⠀⠀⠈⢀⣤⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⢿⠿⠿⠷⠶⠶⣶⣤⣴⣼⣇⣈⣛⣻⡟⠟⠁⣐⠃⠀⠀⠀⠀⠐⢄⠀⠀⠀⡀⢹⢸⠂⠀⢦⠄⣸⣿⢻⣹⠸⣿⣿⣿⠋⢀⣾⣿⣿⢰⢯⣾⣿⣿⣿⣅⠀⠐⠁⠀⠀⠀⠀⠻⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣭⢍⣭⣭⢭⣥⣤⡄⣤⠄⢤⡤⢀⣠⣤⡤⣤⡤⣤⢤⡄⢨⡤⠀⠀⡤⣤⠭⣥⢬⡥⣤⢽⡯⣥⢀⣬⢿⣿⢥⡤⣬⡥⣤⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠠⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠹⠼⢹⠯⠿⣸⠇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡐⢤⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣤⢢⡤⣤⠱⣦⣤⣤⢤⡤⣤⢭⡤⣴⠟⢡⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⠀⢃⣿⢀⣿⢩⣏⣸⣟⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⣼⣿⣿⣩⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢾⣿⣿⠟⠁⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡟⠿⣿⣿⣿⣿⣿⠋⠉⠋⠁⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠨⣿⣿⡿⢻⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⢀⠀⡀⣀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⢾⣗⣌⣠⣬⣿⣿⣿⣿⣧⣤⣶⣶⠆⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠸⣶⣤⣙⣷⣄⠀⠀⠀⠀⠀⠘⣿⠀⣿⢿⠇⢸⣿⣿⣟⠅⠈⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣇⢑⠛⠛⠁⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⡿⠀⣿⣶⠀⠸⢿⣿⣿⣿⣶⠶⠀⠀⠀⠀⠠⣴⣽⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⣿⠿⡧⠄⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣁⢰⣜⡉⢉⣍⣉⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠁⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠗⠓⣀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⢛⣿⡉⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⠀⢠⣤⣀⠁⢀⣀⡀⠀ ⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⠳⠤⠌⠈⣦⣔⣂⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣷⣽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠙⠉⠀⠀ ⠀⠀⠀⠼⠿⡟⠉⠁⠀⠀⣼⣧⣀⡳⣶⣄⠀⣀⣶⣟⣻⣿⣿⣿⢷⡀⠀⠀⢀⡀⠘⡟⠋⢹⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣯⠉⠻⣿⣿⣿⣿⣾⣿⡿⣏⠟⠉⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣀⣴⡇⠀⠀⠀⠁⢂⡀⠀⠰⣪⣿⣿⣿⣿⣿⠛⢀⠇⠀⠈⣹⡄⠀⠙⠃⠼⠳⣶⢸⡁⠀⣤⠄⠀⣰⣿⣽⢸⣿⣟⣯⣄⣐⠿⢿⣿⡿⣿⡏⡄⢻⣧⠉⠉⠀⣠⠀⠀⠀⠈⢀⣠⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⢿⣿⠿⠷⠶⠶⣶⣤⣴⣾⣇⣈⡛⢻⡟⠟⠁⣐⠃⢀⠀⠀⠀⠐⢄⠀⠀⠀⢃⢹⠻⡇⠀⠆⡄⣰⣿⢿⣿⠸⣿⣿⣿⠟⢀⣾⣿⣿⢡⣏⣾⣿⣿⣿⣅⠀⠀⠃⠀⠀⠀⠀⢾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣭⢍⣭⣭⢭⣥⣤⡄⣤⠄⢤⡤⢀⣠⣤⡤⣬⡤⣤⣤⡌⢨⡤⠀⠀⡤⣥⠭⣥⢬⡧⣤⢼⡯⣤⢀⣬⢽⣿⢯⡤⣬⡥⣤⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⠀⠸⠏⡰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⠇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢦⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣤⢢⡤⣤⠫⣦⣤⣤⢤⡤⣤⢭⡥⣴⠛⢡⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢀⢂⣿⢀⣿⢩⣏⣸⣟⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡆⠀⠀⠀⠀⠀⣤⣾⣿⣆⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⡿⡿⠟⠉⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠂⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⡟⣝⣿⡛⠿⣿⣿⣿⣿⣿⠛⠛⠉⠁⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⣿⣿⡿⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣬⣿⣿⣿⣿⣶⣤⣦⣤⠤⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠨⣷⣄⣘⣷⣄⠀⠀⠀⠀⠀⠘⣿⠀⣿⣿⡇⢸⣿⣿⡟⠅⠀⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣾⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣇⢈⠻⠛⠃⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣷⣿⣿⣿⣿⡀⠀⠀⠀⠀⠰⠿⠀⣿⣷⠂⢸⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣦⡄⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣑⣠⣜⡛⢉⣭⠉⡅⠀⠀⠀⠀⠀⠀⠀⠘⠐⠁⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠁⠉⠻⠗⠒⣀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠉⠛⣿⡛⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⠀⠀⣤⣂⡁⠀⡀⠀⠀ ⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⠳⠧⠜⠀⣦⣐⣢⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⡇⠀⠀⠀⠀⠀⠁⣈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⣽⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠋⠛⠛⠉⠀⠀ ⠀⠀⠀⠴⠿⡿⠉⠉⠉⠀⣼⣇⣘⡳⣶⣄⠀⢄⣴⣟⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⡿⠓⢹⣧⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣯⠉⠻⣿⣿⣿⣿⣾⣿⡿⡯⠟⠋⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣤⣀⣴⡇⠀⠀⠀⠀⢀⡀⠀⢠⣬⣿⣿⣿⣿⣿⠟⢁⣟⠈⠈⣻⣀⠀⠘⠇⡄⡷⣰⠘⡇⠀⣀⡀⠀⣰⣿⣿⢸⣿⣟⣻⣁⣀⢿⢿⣿⣯⣿⡟⡀⢹⣦⠚⠁⠀⣀⠀⠀⠀⠈⠀⣀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣿⣿⠷⠶⢶⣦⣤⣴⣶⣶⡉⡛⢿⡿⠝⠁⣐⠊⢀⠀⠀⠀⠐⠀⠀⠀⠀⢅⢹⡿⡇⠀⠀⡄⢰⣿⣿⣿⠸⣿⣿⣿⡟⠁⣴⣾⣿⢃⡟⣴⡿⣾⣟⣃⠀⠀⠇⠀⠀⠀⠀⣾⠟⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣭⢍⣭⣭⢭⣤⣤⡄⣤⠄⢤⡤⠀⣠⢤⡤⣤⡤⣤⣤⡌⢨⡤⠀⠀⡤⣥⠭⣥⢬⡧⣤⢼⡧⣥⢀⣤⢽⣿⢯⡤⣤⡭⣤⠬⡭⣭⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠤⠸⠧⠄⠀⠸⠏⡰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢤⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣼⢣⡤⣤⠫⣷⣤⣤⢤⡤⣤⢭⡥⣤⠻⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⢀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢀⣂⣿⢀⣿⢩⣏⣸⣟⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡆⠀⠀⠀⠀⠀⣀⣴⣍⣒⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⠀ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢐⣿⣿⠿⠋⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⡟⣝⣿⡛⠿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠀⠀ ⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣬⣿⣿⣿⣿⣦⣤⣤⣠⣄⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠨⢴⣤⣈⣲⣤⠀⠀⠀⠀⠀⠘⢿⡇⣾⣿⡷⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⢮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣋⠈⠹⠛⠗⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠀⢼⡧⠃⠈⣿⣿⣿⣶⣶⡤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣲⣄⢾⢿⣿⣿⡿⣶⡀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣅⡠⣾⣛⠉⣩⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣿⢿⣿⣭⣑⢣⣿⡿⠁⠉⠻⠟⠒⣂⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠛⣿⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠾⠟⠋⠉⠉⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⠳⢦⠼⠀⣤⡀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠊⢘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠛⠋⠀⠀ ⠀⠀⠀⠰⠿⡿⠛⠉⠉⠉⣹⣇⠈⡳⣤⡀⠀⠄⣤⣿⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠿⠛⠛⣧⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣯⠙⠻⣿⣿⣿⣿⣾⣿⣿⡹⠛⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣦⣄⣀⣠⡇⠀⠀⠀⠀⢉⠀⠈⢀⣬⣿⣿⣿⣿⣿⠟⠁⣾⠉⠈⣳⣀⠀⠀⠑⠀⣳⢰⡀⡏⠀⣀⡀⠀⢠⣾⣟⢸⣿⣿⣛⣁⡀⢾⣿⣿⣿⢿⡿⠁⢸⣄⠐⠂⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⢿⣿⣿⣿⣶⠦⣤⣤⣤⣑⣖⣾⠉⠛⠻⣿⠹⠃⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡏⡇⠀⢘⡀⢀⣿⣟⡿⠸⣿⣿⣿⡿⠉⣠⣺⣿⠏⡾⣵⡷⣾⣿⣀⠀⠠⠁⠀⠀⠀⢀⣾⠧⠐⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣭⢍⣭⣭⢥⣤⣥⡄⣤⠄⢤⡤⠀⢠⢤⡤⣤⡤⣤⢤⡌⢠⡤⠀⠀⡤⣤⠬⣭⢤⡦⣤⢬⡧⣤⢀⣤⢭⣿⢯⡤⣤⡭⣥⠭⡭⣭⢤⣤⣄⣤⣤⣤⣌⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠍⠁⠼⠇⠸⠏⠇⠿⠠⠸⠧⣼⣄⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡐⢤⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣬⢫⡤⣤⠻⣭⣤⣤⢤⡤⣤⢼⡥⣤⠿⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⢀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣰⢆⣿⠀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡆⠀⠀⠀⠀⠀⣀⣴⣆⣧⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠄ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠿⢿⠟⠛⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⡿⡛⠛⠛⠉⠁⠀⠀ ⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⢻⣿⣿⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣦⣤⣤⣤⣄⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠡⣵⣦⣨⣲⣤⠀⠀⠀⠀⠀⠈⢻⡇⣹⡿⣿⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣾⢭⣿⣷⣿⣮⣿⢿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣏⡀⠙⠛⠏⠁⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢨⠀⢹⣧⡆⠀⢿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⣿⡷⡀⡂⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣍⣢⣿⣋⢉⣩⡉⡅⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣿⢿⣟⣭⣱⢲⣿⡿⠁⠉⠻⠟⠒⣂⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢻⣿⡏⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠾⠟⠋⠉⠉⠀⠀⠀⠠⣀⣀⠁⠀⢀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⠻⠧⠴⠀⣤⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠛⠛⠛⠃⠑⠁⠀ ⠀⠀⠀⢠⢿⡿⠛⠋⢉⠉⣹⣇⠋⠷⣦⡀⠀⠄⣠⣿⠿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⢿⠟⠋⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣯⠙⠻⣿⣿⣿⣿⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣤⣄⣀⣠⡇⠀⠀⠀⠂⠉⠀⠉⢉⣨⣿⣿⣿⣿⣿⡿⠁⣿⠉⠈⢳⡀⠀⠐⠁⠀⢱⢤⡗⡏⠀⢀⣀⠀⢀⣾⡟⢻⣿⣿⣟⣁⠀⢾⣿⣿⣿⢽⡿⠁⢰⡄⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⣿⣿⣿⣿⣶⣦⣤⣤⣌⣙⣖⣾⠙⠻⠻⣿⠽⠋⠀⠖⠈⠀⠀⠈⠉⠀⠀⠀⠀⣆⢸⡏⡇⠀⢨⡀⢀⣾⣿⡟⡾⣿⣿⣿⡿⠉⣰⣾⣿⡏⣾⣡⣷⣮⣷⣀⠀⠰⠁⠀⠀⠀⢠⢾⠁⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣭⢍⣭⣭⢤⣤⣥⡄⣤⠄⢤⡥⡀⢠⢤⡤⣤⡤⣤⣤⡬⢠⡥⡆⠀⡤⣤⠬⣭⢤⡦⣥⢬⡯⣤⢀⣤⢭⣿⢯⡤⣤⡭⣥⠭⡭⣭⢤⣤⣄⣤⣤⣤⣍⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠌⠁⠼⠇⠸⠯⠇⠿⠤⠸⠧⢽⣄⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡒⢤⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣬⢡⡤⣤⠛⣭⣤⣤⢤⡤⣤⢼⡥⣤⠿⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⢀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢹⣀⣿⢀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⡆⠀⠀⠀⠀⠀⣀⣄⣤⣃⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⡃ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠿⣿⡿⠋⢨⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⡿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡘⠟⣝⣿⡛⠿⣿⣿⣿⣿⡿⠛⠛⠛⠋⠁⠀⠀ ⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⢻⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣶⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣶⣦⣤⣤⣆⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠣⣴⣦⣌⣳⣤⠀⠀⠀⠀⠀⠈⢻⡇⢸⡿⣿⠘⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣏⠁⠘⠛⠛⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠃⢸⡧⠋⠀⣿⣿⣿⣶⣶⣤⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⣿⣶⢀⣀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣎⣶⣿⣍⣉⣽⣉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣿⢿⣟⣭⣑⢣⣿⡿⠁⠉⠻⠟⠒⣂⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⣻⡿⠍⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠾⠟⠋⠉⠉⠀⠀⠀⠀⢀⢀⠁⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⠻⠿⠾⠀⣄⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠛⠛⠛⠒⠛⠀⠀ ⠀⠀⠀⢠⢿⡿⠛⠋⠉⠉⢱⣇⠀⢳⣦⡀⠀⠄⣠⣿⠿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⢿⠟⠫⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠙⠻⣿⣿⣿⣿⣾⣿⣟⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣤⣄⣀⣠⡇⠀⠀⠀⠂⠉⠁⠉⢉⣨⣿⣿⣿⣿⣿⡿⠃⣻⠙⠉⢳⣄⠀⠀⠁⠀⢰⢤⡗⡏⠀⢀⣀⠀⢀⣾⡟⣿⣿⣿⣟⣃⠀⢾⣿⣿⣿⢽⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⣿⣿⣿⣿⣶⣦⣤⣤⣌⣙⣖⣾⠙⠻⠻⣿⠽⠋⠀⠖⠀⠀⠀⠈⠉⠄⠀⠀⠀⠀⣸⣯⡇⠀⢨⡀⢀⣾⣿⡟⡷⣿⣿⣿⡿⠋⢰⣼⣿⡏⣾⣡⣷⣮⣧⡀⠀⠘⠀⠀⠀⠀⣤⣖⠠⠴⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢍⣭⣭⢤⣤⣥⡄⣤⠄⢤⡤⣄⢠⢤⡤⣤⡤⣤⣤⡄⢠⡽⠁⠀⡤⣤⠬⣭⢥⡤⣥⢬⡯⣤⢀⣤⢭⣿⢯⡤⣤⡭⣥⠭⡭⣥⢤⣤⣄⣤⣤⣤⣍⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠡⠍⠁⠼⠇⠸⠏⠇⠿⠤⠸⠧⠼⣆⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣼⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡐⢤⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣤⢠⡤⣤⠛⣭⣤⣤⢤⡤⣤⢼⡭⣤⠿⢡⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⢀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢠⢀⣿⣀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡆⠀⠀⠀⠀⠀⢀⣤⣆⣳⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡂ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⢿⣿⡟⠏⢈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⡿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡚⡟⣝⣿⡛⠿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀ ⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⢻⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣧⣤⣤⣤⣤⣀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠡⣴⣦⣬⣽⣦⡀⠀⠀⠀⠀⠈⢻⡇⣸⣿⣟⠘⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣷⣿⢮⣿⣿⣟⡙⡻⣿⣿⡝⠋⢿⣿⣿⣏⠁⠙⠛⠻⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢈⠁⠹⣧⠊⠀⢿⣿⣿⣾⣶⡦⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣲⣄⢾⢿⣿⣿⣿⡴⠤⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣭⣠⣼⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣻⢿⣿⣭⣑⢳⣿⡿⠁⠉⠻⠟⠒⣀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣯⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠾⠟⠋⠉⠉⠀⠀⢀⠀⣀⣀⠁⠀⢀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀⠉⠛⠟⠟⠀⣤⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⠀⠀⠀⠀⠀⠊⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠛⠙⠛⠛⠋⠀⠀ ⠀⠀⠀⠰⠿⡿⠛⠉⠉⠉⣱⣇⠀⠻⣷⣄⠀⠄⣠⣟⠿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠿⠛⠋⣿⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⠙⠻⣿⣿⣿⣿⣾⣿⣿⡟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⣄⣀⣠⡇⠀⠀⠀⠀⠉⠀⠈⢉⣬⣿⣿⣿⣿⣿⡿⠁⣾⠙⠉⢳⣄⠀⠀⠃⠀⣰⣤⡗⡏⠀⢀⣀⠀⢀⣾⡟⡿⣿⣿⣟⣁⡀⢾⣿⣿⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⢿⣿⣿⣿⣶⠶⣤⣤⣤⣝⣒⣶⠉⠛⠻⣿⠻⠋⠀⠒⢀⠀⠀⠀⠀⢄⠀⠀⠀⠄⣾⣿⡇⠀⢘⡀⢀⣾⣿⡟⡗⣿⣿⣿⡿⠋⣰⣾⣿⡏⡾⣱⡷⣶⣦⡀⠀⠆⠀⠀⠀⢀⣴⡆⠠⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢍⣭⣭⢥⣤⣤⡄⣤⠔⢦⡾⣄⣠⢤⡤⣤⡤⣤⣤⡄⢩⡭⠀⠀⡤⣤⠬⣭⢤⡮⣥⢬⡯⣭⢀⣤⢽⣿⢯⡤⣤⡭⣥⠬⡭⣥⢤⣤⣄⣤⣤⣬⣌⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⡎⠀⠼⠇⠸⠏⠇⠿⠤⠸⠧⠴⡄⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡐⢤⡄⢤⢤⡤⣄⠀⢠⡤⣤⢀⡤⣶⢲⡤⣤⠻⣭⣤⣤⢤⡤⣤⢼⡥⣤⠿⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⢀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢐⣀⣿⢀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡆⠀⠀⠀⠀⠀⣠⣠⣖⣳⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅ ⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠿⣿⡟⠓⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡚⠟⣝⣿⡛⠿⣿⣿⣿⣿⣿⠟⠛⠛⠁⠀⠀⠀ ⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢿⣿⣿⢻⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⡀⢀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣬⣿⣿⣿⣿⣿⣷⣦⣤⣦⡄⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⣶⣷⣶⣽⣦⡀⠀⠀⠀⠀⠀⢻⡇⢹⣿⣿⠘⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣯⡀⠙⠛⠛⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⡃⠘⢧⡆⠀⢻⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⢿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⣿⡿⣔⠦⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⡿⢿⣶⣴⣾⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣻⢿⣟⣭⣑⢳⣿⡿⠉⠉⠻⠟⠒⣀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⡂⢘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣯⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⣀⡀⢀⣀⡁⠀⢀⡀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⠀⣄⡈⠙⠛⠋⠀⣦⣐⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠂⠀⠀⠀⠀⠀⠀⠙⠓⠉⠛⠋⠛⠛⠁⠀ ⠀⠀⠀⠰⠿⡿⠉⠉⠩⠉⣰⣏⡀⣻⣿⣄⡀⣄⣤⣟⣻⣿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠻⠛⠋⣿⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⡙⠻⣿⣿⣿⣿⣾⡿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣤⣄⣠⡇⠀⠀⠈⠁⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠁⣸⠉⠈⣹⣄⠀⠈⠁⠀⣿⣶⣇⡏⠀⢀⡀⠀⢀⣾⣏⡿⣿⣿⣻⣅⣀⠺⣿⣿⣿⢿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⠿⠶⠶⢦⣤⣭⣖⣶⡉⠛⠟⣿⠩⠫⣤⣾⣃⡀⠀⠀⠀⢤⠀⠀⠀⢙⣿⡟⡇⠀⢰⡠⢀⣾⣿⡟⡏⣿⣿⣿⡿⠁⣰⣺⣿⡏⡾⣵⡾⣧⣀⠀⠀⠀⠀⠀⠀⣤⠆⢠⡴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢍⣭⣭⢭⣤⣬⡄⣤⠏⢭⡬⣿⣤⢤⡤⣤⡥⣤⣤⡄⢨⡥⠀⠀⡤⣤⠬⣭⢤⡯⣤⢬⡯⣭⢀⣤⢽⣿⢯⡤⣤⡭⣥⠤⡥⣤⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠠⠿⠤⠾⠡⠄⠀⠼⠇⠸⠏⠇⠿⠠⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡐⢦⡄⢤⢤⡤⣄⠀⢠⡤⣤⢘⡯⣿⢲⡤⣤⠺⢵⣤⣤⢤⡤⣤⢬⡥⣬⠿⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣨⣆⣿⠀⣿⢩⣏⣸⣏⡷⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⡆⠀⠀⠀⠀⠀⢠⣴⣶⣥⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆ ⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⡟⠃⢸⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣿⣿⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣪⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⣾⣷⣶⣿⣶⡀⠀⠀⠀⠀⠀⢻⡇⢹⡿⣿⠈⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⡀⠘⠛⠛⠂⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⣿⣿⠿⢿⠿⡇⠀⠀⠀⠀⠀⠸⠅⠸⠇⠂⠀⠻⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⡿⡆⠤⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡿⢿⣶⣶⣾⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣑⢳⣿⡿⠉⠉⠻⠟⠓⣂⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡗⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠾⠟⠋⠉⠉⠀⢀⣀⣀⣄⣂⠁⠀⣀⡀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣟⠀⣤⡀⠉⠉⠋⠀⣦⣔⣂⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠋⠁⠐⠀⠀⠀⠀⠀⠀⠈⠛⠁⠙⠋⠉⠓⠉⠀⠀ ⠀⠀⠀⠰⠿⢿⠉⠉⢩⠁⣰⣏⣐⣹⣿⣦⣀⣄⣴⣟⣛⣿⣻⣿⣷⡀⠀⠀⠀⠀⠀⡻⠛⠀⣿⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⡉⠻⣿⣿⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣦⣄⣠⣇⠀⠀⠀⠈⠀⡀⠀⠀⣤⣿⣿⣿⣿⣿⠟⠁⣸⠈⠀⢹⣆⠀⠈⠩⢘⣿⣶⡇⡏⠀⢠⡄⠀⢀⣾⣏⡟⣿⣿⣻⣅⣀⠻⢿⣿⣿⢺⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⠿⢿⣿⡿⠿⠷⠶⢶⣦⣬⣶⣾⣌⡛⠙⣿⠹⠛⣲⣾⣥⡀⠀⠀⠀⠦⡀⠀⠈⢽⣿⡏⡗⠀⢰⡠⢀⣿⡿⡿⡇⢿⣿⣿⡿⠁⣰⣾⣿⡇⡿⣵⡿⣦⡀⠀⠀⠀⠀⠀⢀⣴⠂⣠⡴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢍⣭⣭⢭⣥⣬⡄⣬⠅⢤⡼⢿⣦⢤⡤⣤⡭⣤⣤⡄⢩⡥⠀⠀⡤⣤⠬⣭⢤⡯⣤⢬⡿⣭⢀⣤⢽⣿⢯⡤⣤⡭⣤⠤⡥⣤⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠡⠄⠀⠼⠇⠸⠏⠇⠿⠠⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢦⡄⢤⢤⡤⣄⠀⢠⡤⣴⢆⡾⣯⢰⡤⣴⠺⣵⣤⣤⢥⡤⣤⢭⡥⣬⠻⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⠈⢀⣿⠀⣿⢩⣏⣸⣏⡇⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⠗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⠀⠀⠀⠀⠀⣠⣴⣦⣭⣟⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣿⡿⠋⢈⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⠄⠠⢸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡚⢟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣏⡉⠉⠁⠀⠀⠀ ⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢿⣿⣿⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣁⣀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢾⣗⣌⣠⣨⣿⣿⣿⣿⣿⣶⣶⣴⣶⡤⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠑⣾⣷⣶⣾⣷⡄⠀⠀⠀⠀⠀⢻⡇⢸⣿⣿⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⡀⠉⠙⠛⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢇⡀⣿⡿⠿⢿⠿⡇⠀⠀⠀⠀⠀⢸⠇⠸⣳⢆⠀⠻⣿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⢿⣿⣿⡿⠶⠦⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡿⢿⣶⣶⣿⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣻⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠟⠒⣀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡗⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣵⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⣄⣄⣀⣠⣀⡁⡀⣀⡀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢟⠀⣤⡀⠉⠉⠉⠀⣦⣔⣂⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⣿⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠈⠉⠉⠁⠋⠀⠀ ⠀⠀⠀⠰⠿⢿⠉⠉⠩⠀⣰⣏⣐⣻⢿⣦⣀⣄⣴⣿⣛⣿⢻⣿⣶⡀⠀⠀⠀⢀⠀⣿⠋⠁⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡙⠻⣿⣿⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣦⣤⣠⣇⠀⠀⠀⠉⠀⣀⠀⠀⣵⣿⣿⣿⣿⣿⠟⠁⣸⠀⠀⢹⣦⠀⠈⠁⢸⣿⣷⡇⡇⠀⢠⠤⠀⢀⣿⣏⡟⣿⣿⣻⣥⣀⠻⢿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠿⠿⠿⠿⠿⠷⠶⠶⣶⣤⣶⣿⣈⡙⠛⣿⠻⠯⣴⣿⣥⡀⠀⠀⠀⠲⡀⠀⠈⠿⣿⡏⠗⠀⢰⡤⢀⣿⡿⣯⡇⢿⣿⣿⡿⠁⣴⣾⣿⠇⡿⣴⡿⣄⠀⠀⠀⠀⠀⠀⣠⡴⠀⡤⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢍⣭⣭⢭⣭⣬⡄⣬⠅⢤⡬⢿⣦⢤⡤⣤⡭⣤⣤⡄⢩⡥⠀⠀⡤⣤⠬⣭⢤⡭⣤⢬⡿⣭⢀⣤⢽⣿⢯⡤⣤⡭⣤⠤⡤⣤⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠠⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢦⡄⢤⢤⡤⣄⠀⢠⡤⣴⢀⡼⣤⢰⡤⣴⠺⢡⣤⣤⢤⡤⣤⢬⡥⣼⣻⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢨⢀⣿⠀⣿⢩⣏⣸⣏⡇⠁⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⠗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠰⣿⣿⡟⠉⢑⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣧⠀⠀⠀⠀⠀⠉⢨⣃⠔⠸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣟⡉⠙⠅⠀⠀⠀ ⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣈⣁⣀⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣬⣿⣿⣿⣿⣷⣿⣶⣾⣶⡅⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣾⣿⣶⣾⣷⡄⠀⠀⠀⠀⠀⢻⡇⢸⣿⣿⠈⣿⣿⣿⣷⠆⠘⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⡤⠙⠛⠛⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⣿⡿⠿⢿⠿⡇⠀⠀⠀⠀⠀⢾⡇⢘⣷⣈⠀⢿⣿⣿⣿⣿⣶⠦⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣶⠦⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡾⢿⣶⣶⣾⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣟⣭⣱⢳⣿⡿⠉⠉⠻⠟⠓⣂⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣽⣿⠗⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⢠⣤⣄⣀⣠⣂⣁⠀⣀⡀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⡀⠉⠉⠉⠀⣶⣄⣒⣠⣄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠋⠁⠂⠀⠀⠀⠀⠀⠀⠻⠛⠋⠉⠋⠙⠙⠋⠁⠀ ⡀⠀⠀⠰⠿⢿⠉⠉⢱⠀⣠⣿⢌⣛⢿⣦⣀⣂⣴⣿⣛⣿⢿⣿⣷⣄⠀⠀⠀⣀⠀⢿⠋⠁⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡙⠻⣿⣿⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢑⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣶⣤⣤⣇⠀⠀⠀⠉⠀⣀⠀⠀⣯⣿⣿⣿⣿⣿⠟⠁⣸⠈⠀⢹⣦⠀⠈⠧⢀⣿⣷⣇⡇⠀⢠⡤⠀⢀⣿⣇⡏⣿⣿⣿⣥⣀⠻⢿⣿⣿⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠻⠿⠿⠿⠿⠿⠶⠶⣶⣶⣷⣿⣍⣙⢛⣿⡻⠋⣠⣞⣁⠀⠀⠀⠀⠳⣄⠀⠈⢹⣿⡟⠟⠀⠰⣴⢀⣿⡿⣯⡇⢿⣿⣿⡿⠁⣴⣿⣿⡇⡿⣴⣇⣀⠀⠀⠀⠀⠀⠀⣠⡖⢀⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢍⣭⣭⢭⣭⣭⡄⣬⠟⢭⡽⣷⣤⢤⡤⣤⡭⣤⢤⡄⢩⡥⠀⠀⡤⣤⠬⣭⢤⡭⣤⢬⡿⣭⢀⣤⢽⣿⢯⡤⣤⡭⣤⠤⡤⣤⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠏⠇⠿⠠⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡄⢤⢤⡤⣄⠀⢠⡤⣴⢀⡴⣤⢰⡤⣼⠚⢶⣤⣤⢤⡤⣤⢤⡤⣤⠹⢧⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢠⢀⣿⠀⣿⢩⣏⣸⣏⡇⠀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⠀⠀⠀⠀⠀⣠⣶⣶⣭⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠿⣿⡿⠋⠀⡟⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂ ⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠍⡥⠄⢸⡧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣏⡉⠝⠁⠀⠀⠀ ⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢹⣿⣿⢿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⢀⢀⣛⣀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣶⣾⣶⣶⡤⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣾⣿⣶⣾⣷⡄⠀⠀⠀⠀⠀⢻⡇⢸⣿⣿⠈⣿⣿⣿⣷⠂⠈⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣅⠉⠛⠛⠁⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⡀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠸⠇⠸⢳⠭⠀⠚⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⡧⢦⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡾⢿⣶⣴⣾⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣽⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠁⠉⠻⠟⠛⣊⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⢒⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⢐⣀⣄⣀⣤⣦⣁⢀⣀⡀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠃⣠⡀⠉⠛⠋⠀⢳⣄⣐⣢⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⠋⠋⠘⠋⠛⠛⠉⠁⠀ ⣀⠀⠀⠐⠛⢿⠋⠉⢑⠀⢠⣿⢄⣘⢿⣦⣀⣀⣴⣾⣛⣿⢿⣿⡿⣄⠀⠀⠀⣀⠀⢿⠋⡁⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡍⠻⣿⣿⣿⣯⣺⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠄⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣤⣴⣿⡀⠀⠀⠈⠀⣀⠀⠀⣦⣿⣿⣿⣿⣿⡟⠁⡸⠀⠀⢹⣧⠀⠀⠩⠀⢹⣶⣇⡇⠀⢠⡤⠀⢀⣾⣧⡏⣿⣿⣿⣥⣀⠻⢿⣿⣿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⠛⠿⠿⠿⠿⠛⠒⠶⣶⣶⣿⣿⣏⣙⣻⢿⡻⠋⢀⡚⠁⠀⠀⠀⠀⠓⣄⠀⠀⠈⣻⡟⡿⠀⠰⢴⢀⣿⡿⣿⣧⣿⣿⣿⡿⠁⣴⣿⣿⡇⡾⣴⡄⠀⠀⠀⠀⠀⠀⠀⣠⡔⢀⣤⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⢍⣭⣭⢭⣭⣭⡅⣤⠅⢤⡤⡀⣠⢤⡤⣤⡭⣤⣤⡄⢠⡥⠀⠀⡤⣤⠬⣭⢤⡭⣭⢥⡤⣤⢁⣤⢽⣿⢯⡤⣤⡭⣤⠤⡤⣤⢤⣤⣄⣤⣥⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⡏⠀⠼⠇⠸⠏⠇⠿⠠⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⠘⠃⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡄⢤⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢰⡤⣼⠛⢶⣤⣤⢤⡤⣤⢥⡤⣤⠀⢠⡥⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢠⢀⣿⠀⣿⢩⣏⣸⣟⡷⡀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒ ⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⣿⣿⡿⠉⢡⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂ ⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠈⢉⣿⢬⣸⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⡟⡉⢛⡁⠀⠀⠀ ⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⣿⣇⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⢈⣛⣉⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⡿⣷⣾⣾⡧⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣶⣾⣷⣄⠀⠀⠀⠀⠀⢻⡇⢹⣿⣿⠀⣿⣿⣿⣿⠖⠒⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣾⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⡤⠋⠙⠛⠁⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⡀⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠾⠇⠈⣳⢽⠀⠺⣿⣿⣿⣿⣷⠢⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣷⠄⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⢿⣶⣤⣾⣤⣼⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣟⣭⣑⢳⣿⡿⠉⠉⠻⠟⠛⣊⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⢖⡺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⢰⣤⣄⣀⣴⣦⣁⣀⣀⣀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⡃⢀⡀⠉⠓⠋⠀⢰⣦⣁⣂⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⠋⠋⠙⠋⠛⠙⠋⠀⠀ ⣀⠀⠀⠐⠛⢿⠏⠉⠐⠂⢀⣿⢅⣘⡿⣦⣀⣀⣰⣾⣛⣻⣿⢿⡿⣆⠀⠀⢀⣀⠀⡻⠋⠁⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡍⠻⣿⣿⣿⣯⢺⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠄⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣦⣴⣿⡀⠀⠀⠀⠁⣀⡀⠀⣬⣿⣿⣿⣿⣿⡿⠃⣸⡇⠀⠩⢧⠀⠀⠁⠀⣻⣷⡧⡇⠀⢠⡤⠀⢀⣾⣯⡇⣿⣿⣿⣥⣀⠻⠿⣿⣿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠿⠿⠿⠟⠛⠓⠶⢶⣶⣿⣿⣧⣝⣛⣿⣟⠋⢀⣚⠁⠀⠀⠀⠀⠑⡄⠀⠀⢈⣻⣿⠿⠀⠰⢴⢀⣿⡿⣯⣧⡿⠿⠻⢿⡅⣴⣿⣿⡇⡿⣴⡄⠀⠀⠀⠀⠀⠀⠀⣀⡔⢀⣤⣶⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⢍⣭⣭⢭⣭⣭⡅⣤⠄⢤⡤⠀⣠⢤⡤⣤⡭⣤⣤⡄⢠⡥⠀⠀⡤⣬⠬⣭⢤⡽⣬⢤⡬⣭⢉⣥⢽⣿⢯⡤⣤⡭⣤⠤⡤⣤⢤⣤⣄⣤⣭⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⡆⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⠀⠁⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢭⡅⢤⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢰⡤⣼⠻⢲⣤⣤⢤⡤⣤⢭⡥⣤⠀⢠⡥⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢠⢀⣿⢀⣿⢩⣏⣸⣿⡷⡀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⠀⠀⠀⠀⠀⢠⣤⣿⣶⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢾⣿⡿⠿⠁⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⡄⠀⠀⠀⠀⠐⢹⣷⠄⢐⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣟⡋⠉⠁⠀⠀⠀ ⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢈⡙⢂⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣾⣷⣿⣦⣦⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣾⣿⣶⣾⣷⣦⠀⠀⠀⠀⠀⢻⡇⢸⣿⣿⠂⢹⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⡅⠈⠙⠛⠁⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⠇⠈⠣⠾⠀⠈⣿⣿⣿⣿⣶⡦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣶⡧⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣼⢿⣶⣤⣾⣤⣴⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣿⢿⣿⣭⣑⢳⣿⡿⠁⠉⠻⠟⠓⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣗⡘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡷⠿⠟⠋⠉⠉⢰⣤⣀⣀⣠⣦⣁⣀⢀⣀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⡀⠈⠛⠚⠁⠸⣦⣀⣒⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣿⡆⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⡏⠛⠛⠋⠉⠙⠉⠁⠀ ⣀⠀⠀⠀⠛⢻⡏⠉⠀⠀⢂⣼⠧⣀⡿⣦⣀⠀⣠⣾⣛⣻⣯⣿⡿⣦⡀⠀⠀⣀⠀⠹⠋⠁⢻⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡍⠻⣿⣿⣿⣯⣺⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣶⣦⣤⣿⡁⠀⠀⠀⠑⢀⡀⠀⣬⣾⣿⣿⣿⣿⡿⠋⢀⡇⠁⢈⡷⠀⠀⠈⠀⢸⣷⣿⣿⠀⢠⡤⠀⢀⣾⣿⡇⣿⣿⣿⣥⣀⡹⠿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠻⠿⠿⠟⠛⠛⠶⢶⣶⣾⣽⣧⣽⣿⣿⣟⠟⠁⠐⠋⢀⠀⠀⠀⠑⡄⠀⠀⠈⣹⣿⣾⠀⠠⢦⠀⣾⡿⣿⡇⢿⡿⣛⣛⣧⣴⣿⣿⡏⣼⣱⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢍⣭⣭⢭⣭⣭⡅⣤⠄⢤⡤⠀⢠⢤⡤⣤⡬⣤⣤⡄⢠⡥⠀⠀⡤⣬⠬⣭⢥⡼⣤⢤⡦⣥⢀⣭⠌⢿⢯⡥⣤⡭⣤⠤⡤⣤⢤⣤⣄⣤⣬⣥⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⢥⣄⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⠀⠀⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢭⡌⢤⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢰⡤⣬⠛⢰⣤⣤⢤⡤⣤⢭⡥⣤⠀⢠⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⢻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢠⢀⣿⢀⣿⢩⣏⣸⣟⡷⡀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⠀⠀⠀⠀⠀⣠⣤⣶⣾⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣋⣲⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠓⠕⣿⣵⡘⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠁⠀ ⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⡟⣿⣿⣿⣷⣿⣿⡆⠀⠀⠀⠀⠀⢐⢊⣀⣴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣾⣦⡴⣿⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣺⣻⣶⣼⣿⣦⠀⠀⠀⠀⠀⢻⡏⠘⣿⣿⠇⢹⣿⣿⣿⡇⠒⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⢮⣿⣿⣟⡙⡻⣿⣿⡝⠋⢿⣿⣿⣿⡥⠈⠛⠋⠁⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⡇⠀⡭⠬⠀⠈⣿⣿⣿⣷⣷⡦⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣦⠄⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣮⠾⣦⣤⣾⣦⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣭⣑⢳⣿⡿⠉⠉⠻⠟⠛⣃⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⣿⣗⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠿⠟⠋⠉⠉⢰⣤⣄⡀⢀⣢⣁⣀⢀⣀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠈⠛⠚⠁⠀⣷⣄⣐⣠⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠋⠙⠉⠋⠛⠁⠀ ⣀⡀⠀⠀⠛⢻⣿⠁⠀⢐⡠⣰⣿⣜⡙⢷⣄⠀⢀⣶⣟⣻⣿⣿⢿⢷⡀⠀⠀⢀⠀⠹⠏⢉⢽⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣍⠻⣿⣿⣿⣯⣺⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣤⣾⣇⠀⠀⠀⠀⢀⡀⠀⢠⣾⣿⣿⣿⣿⣟⠟⠁⡺⠀⠈⡹⡆⠀⠘⠀⢸⣷⣿⣹⠀⢀⡤⠀⢀⣼⣿⡇⣿⣿⣿⣥⣀⡸⠿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠻⠿⠿⠿⠛⠚⠲⢶⣶⣾⣿⣧⣹⣿⡿⡿⠽⠁⠐⠚⠀⠀⠀⠀⠈⢆⠀⠀⠈⣹⣿⢻⠀⠀⢦⠀⣼⣿⣻⣇⢻⣿⣿⣿⣿⣤⣿⣿⡟⣸⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢀⣤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢌⣭⣭⢭⣭⣭⡅⣤⠄⢤⡤⠀⢠⢤⡤⣤⡬⣤⣤⡄⢨⡭⠈⠀⡤⣤⠤⣭⢥⡽⣤⢤⡽⣬⢉⣭⠍⢸⢯⡥⣤⡭⣤⠤⡤⣤⢤⣤⣄⣤⣬⣥⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⢄⠀⠼⠇⠸⠏⠇⠿⠤⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⠀⠀⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢬⡍⢤⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢰⡤⣬⢓⢱⣦⣤⢤⡤⣤⢬⡥⣤⠀⢠⡬⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⢻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢀⢀⣿⢀⣿⢩⣏⣸⣟⡷⡀⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⠀⠀⠀⠀⠀⣠⣴⣾⣶⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⡄⠀⠀⠀⠀⠀⠡⣻⣷⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⡿⠉⠉⠉⣀⢀⠀ ⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⢼⣿⣿⡿⣿⣿⣿⣷⣿⣿⠇⠀⠀⠀⠀⠀⢈⢙⢓⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣶⣾⣶⣿⠆ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣷⣾⣿⣶⡄⠀⠀⠀⠀⠹⣿⠘⣿⣿⠇⢹⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢿⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣿⣏⡑⠛⠛⠃⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠸⡿⠀⣿⠾⠆⠘⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣷⠄⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡽⣦⣤⣼⣦⣴⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠻⣛⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⡗⡐⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠐⣦⣄⣠⢰⣶⣅⣀⣀⣀⡀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⡀⢀⠀⠙⠛⠉⠀⢻⣶⣁⣂⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠊⠙⠉⠙⠻⠋⠁ ⣀⡀⠀⠀⠚⢻⣿⠃⠀⠠⠀⢠⡿⣄⡩⢷⣄⡀⢀⣼⣾⣛⣿⣿⣻⡷⣆⠀⠀⢀⡀⢸⡟⢉⢼⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣟⠻⣿⣿⣿⣯⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡒⠂⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣤⣾⣟⠀⠀⠀⠀⠀⣀⠀⢰⣾⣿⣿⣿⣿⣿⡿⠃⡸⠀⠁⡩⡧⠀⠘⠀⣸⣷⣿⣾⠀⠀⡤⠄⠀⣼⣿⣹⣿⣿⣿⣯⣄⡘⠿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠉⠉⠛⠻⠿⠿⠿⠟⠛⠓⢶⣶⣾⣿⣯⣬⣿⣿⣿⡿⠋⠀⠒⠃⠀⠀⠀⠈⢳⠀⠀⠈⣻⣿⠻⠀⠀⢦⠆⣼⣿⢿⣿⠻⣿⣿⣿⣿⣤⣷⣿⡿⣸⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣠⡴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢍⣭⣭⢭⣭⣭⡍⣤⠄⢤⡤⠀⢠⢤⡤⣤⡤⣥⣤⡄⢨⡭⠀⠀⡤⣤⠤⣭⢥⡼⣥⢤⡽⣭⢉⣭⠟⢫⢭⡥⣤⡬⣥⠤⡤⣤⢤⣤⣄⣤⣤⣭⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠤⠀⠼⠇⠸⠏⠇⠿⠤⠸⠧⠄⠀⠸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⠀⠀⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢬⡟⢤⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢡⡦⣬⢳⢱⣦⣤⢤⡤⣤⢬⡭⣤⠈⢡⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⣏⢻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣠⢀⣿⢀⣿⢩⣏⣸⣟⡷⡀⣼⡛⢡⣿⣻⣸⡙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡆⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢫⣿⢿⡾⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⣛⠿⣿⣿⣿⣿⣿⡿⠟⠉⠉⢀⠀⠀ ⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣈⢉⢘⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣷⣷⣾⣶⣷⠄ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣝⣿⣶⣿⣷⣆⠀⠀⠀⠀⠘⣿⠈⣿⣿⡇⢸⣿⣿⣿⣷⠒⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⣿⡙⠛⠟⠓⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⠿⣧⠀⠀⠀⠀⢸⣻⠀⢿⣦⠇⠈⢹⣿⣿⣿⣷⣶⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣷⠆⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣥⢷⣤⣴⣷⣶⡾⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣿⢿⣟⣽⣱⢳⣿⡿⠉⠉⠻⠟⠟⣃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣹⣗⡒⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⣦⣄⣠⣴⣦⣅⣀⢀⣀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⡦⢀⡀⠙⠛⠋⠀⢸⣶⣌⣐⣠⣄⠀⠀⠀⠀⠀⢸⣿⣯⣿⡇⠀⠀⠀⠀⠐⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠙⠛⠉⠙⠛⠋⠀ ⣀⡀⠀⠀⠘⠻⣿⡏⠀⠀⠀⢀⡾⣧⡘⠿⣦⡀⢀⣰⣿⣛⣻⣯⡯⠿⣷⡀⠀⢀⠀⢸⡟⠉⢹⡇⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣟⠻⣿⣿⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣐⠖⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣤⣾⣿⡁⠀⠀⠀⠀⣀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠋⢰⡇⠁⢈⣿⡀⠘⠃⢸⣷⣿⣼⠀⠀⣤⠄⠀⣼⣿⣹⢸⣿⣿⣯⣄⡘⠿⣿⣿⡗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠉⠉⠛⠻⠿⠿⠿⠛⠓⠻⢶⣶⣾⣿⣿⣬⣹⣿⢿⣿⠏⠀⠒⠃⠀⠀⠀⠈⢻⡄⠀⢈⣻⣿⣻⠇⠀⠦⡄⣸⣿⢿⣿⠸⣿⣿⣿⠟⢠⣾⣿⣿⢸⢧⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢍⣭⣭⢭⣭⣭⡍⣤⠄⢤⡤⠀⢠⢤⡤⣤⡤⣭⣤⡄⢨⡭⠈⠀⡤⣤⠥⣭⢥⡬⣧⢤⡼⣯⢁⣤⢽⣿⢯⡥⣤⡼⣥⠤⡤⣤⢤⣤⣄⣤⣤⣭⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠠⠿⠤⠾⠥⡤⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⠀⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⡅⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢬⡝⢤⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢠⡦⣬⢳⢣⣦⣤⢤⡤⣤⢬⡭⣤⠙⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⢻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣠⢀⣿⠀⣿⢩⣏⣸⣟⡷⡀⣼⡛⢡⣿⣻⣸⡙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⡇⠀⠀⠀⠀⢀⣬⣿⣷⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡿⣟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢺⣿⣧⡵⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠀ ⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢈⢋⣉⣵⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⡅ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣜⣿⣷⣿⣿⣦⠀⠀⠀⠀⠸⣿⠀⣿⣿⡟⢸⣿⣿⣿⣷⠒⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣯⡉⠛⠛⠋⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⠿⣿⠄⠀⠀⠀⠸⣿⠀⢙⣧⡇⠀⢻⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣷⠤⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣬⢶⣤⣴⣷⣶⣾⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠁⠉⠻⠟⠻⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣗⢂⢿⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⣦⣄⣠⢰⣦⣅⣀⢀⣀⢀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠿⣧⠀⡀⠙⠛⠋⠁⠘⣷⣎⣕⣢⣤⡀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠐⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠛⠙⠛⠛⠋⠁ ⣀⡀⠀⠀⠘⠛⣿⣿⠁⠀⠀⠠⣵⣿⣌⠛⢦⣀⠀⣠⣷⣟⣻⣿⣿⣿⢿⡀⠀⢀⡀⠸⡟⠉⢹⣇⠀⠀⠀⠀⠀⣺⣿⢿⣿⣿⣟⠻⣿⣿⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠂⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣤⣼⣿⡇⠀⠀⠀⠀⢂⠀⢠⣴⣿⣿⣿⣿⣿⣿⠟⠀⡇⠅⣈⣹⠂⠐⠇⢰⣿⣷⢾⡃⠀⣤⠄⠀⣰⣿⣽⢸⣿⣟⣯⣄⣘⠿⢿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠉⠉⠛⠻⠿⠿⠿⠟⠛⠚⠲⣶⣶⣿⣿⣤⣹⣿⣿⡿⠟⠁⠐⠚⠀⠀⠀⠀⠙⣆⠀⠸⢙⣿⣿⠇⠀⠤⡄⣰⣿⣿⣿⠸⣿⣿⣿⠟⢀⣾⣿⣿⢱⣯⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⣀⣤⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢍⣭⣭⢭⣭⣭⡍⣤⠄⢤⡤⠀⢠⢤⡤⣤⡤⣬⣤⡄⢠⡭⠁⠀⡤⣤⠥⣭⢭⡬⣧⢤⡼⣯⢉⣤⢼⣿⢯⡭⣤⡬⣥⠤⡤⣤⢤⣤⣄⣤⣤⣬⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⢤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠬⠀⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⣇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢬⡟⢤⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢠⡦⣬⢳⢣⣤⣤⢤⡤⣤⢬⡭⣤⡛⢫⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⢻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣠⢀⣿⢀⣿⢩⣏⣸⣟⡷⠆⣼⡛⢡⣿⣻⣸⡙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡇⠀⠀⠀⠀⢠⣼⣿⣷⣽⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢺⣿⣿⡿⢯⣹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠀⠀⠘⠁⣸⣿⡿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⡋⠉⠍⠉⢈⠀ ⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠈⣉⣡⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣈⣿⣷⣾⣿⣶⡄⠀⠀⠀⠘⣿⠁⢿⣿⣟⠨⣿⣿⣿⣿⠒⠂⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⣯⡘⡙⠛⠋⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⠿⢿⡦⠀⠀⠀⠐⢿⠀⠘⣵⡇⠀⣻⣿⣿⣿⣾⣶⠄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣷⠆⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡯⡴⣤⣴⣷⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠟⠟⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⢨⣿⣂⢺⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⢠⣄⣠⣰⣦⣥⣀⡀⣀⡀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⢇⡀⢀⠈⠛⠛⠁⠀⢿⣶⣭⣒⣤⣀⠀⠀⠀⠀⠸⣿⣿⣿⣟⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠛⠙⠉⠙⠛⠋⠀ ⣀⣀⠀⠀⠐⠛⣿⣿⠁⠀⠒⠀⢠⣿⣄⠚⢷⣄⠀⣀⣾⣾⣛⣿⢽⢿⢿⣆⠀⢀⣀⠀⠿⠋⣙⣿⠀⠀⠀⠀⠀⢺⣿⢿⣿⣿⣿⠻⣿⣿⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣦⣼⣿⡏⠀⠀⠀⠀⢀⡀⠀⢤⣾⣿⣿⣿⣿⣿⠟⠁⣸⠈⢀⣉⢇⠀⠩⢰⣿⣷⣟⡇⠀⣤⠄⠀⣰⣿⣿⢸⣿⣿⣯⣅⣘⠿⢿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠛⠿⠿⠿⠿⠛⠛⠷⢶⣶⣿⣿⣤⣍⣿⡿⣿⡻⠃⠀⠚⠁⠀⠀⠀⠘⣣⠀⠸⢻⣿⡿⡇⠀⠰⡄⢰⣿⣟⣿⡸⣿⣿⣿⠟⢀⣾⣿⣿⢣⡏⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣠⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢌⣭⣭⢭⣭⣭⡍⣥⠄⢤⡤⠀⢠⢤⡤⣤⡤⣬⣥⡄⢠⡥⢃⠀⡤⣤⠤⣭⢭⡬⣧⢤⡬⣿⢉⣤⢼⣯⢯⡭⣤⡬⣥⠤⡤⣤⢤⣤⣄⣤⣤⣤⣍⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠠⠿⠤⠾⠥⢤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⢬⡀⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢬⡟⢧⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢠⡤⣤⢻⢢⣤⣤⢤⡤⣤⢮⡭⣤⡻⢣⡤⣍⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⢻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣠⢀⣿⠀⣿⢩⣏⣸⣏⡷⢆⣼⡛⢡⣿⣻⣸⡙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠠⣼⣷⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣫⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠐⣼⠿⣄⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠉⠀⠀ ⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⡄⣠⡀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢁⢈⣵⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⠄ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣨⣿⣷⣿⣿⣦⠀⠀⠀⠘⢻⡇⢸⡿⣿⠀⣿⣿⣿⣿⠈⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣿⣿⡌⠉⠛⠋⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡈⡿⠿⣿⠿⠿⣷⠄⠀⠀⠀⠟⠁⢘⢲⠆⠀⢿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⢿⠆⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⢶⣵⠿⢶⣾⢿⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠟⠻⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⡂⢺⣿⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⣤⣤⣄⣶⣥⣀⡀⣀⡀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠧⣄⠀⡈⠛⠛⠁⠀⢸⣿⣦⣭⣶⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠉⠙⠋⠉⠉⠋⠀ ⣀⣀⡀⠀⠀⠛⣿⣿⡏⠀⠁⠱⡒⡾⠧⠈⢳⣄⡀⢀⣴⣿⣟⣻⠯⡟⡿⣧⡀⢀⣀⠀⣿⠋⡁⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡁⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣶⣾⣿⣟⡁⠀⠀⠀⠈⠀⠀⠄⣼⣾⣿⣿⣿⣿⠿⠁⢰⡇⠠⠬⠿⡈⠒⣹⣿⣷⣯⡇⠀⢠⠤⠀⣠⣿⣯⣿⣿⣿⣯⣤⣈⠻⢿⣿⡿⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠛⠛⠻⠿⠛⠛⠛⠛⢿⣶⣿⣿⣧⣌⣿⣟⣿⠻⠋⠀⠒⠁⠀⠀⠀⠈⢻⡄⠉⣻⡟⡏⠇⠀⠸⣴⢠⣿⡟⣏⡟⢿⣿⣿⡟⢁⣾⣿⣿⢣⡟⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⢠⡶⣀⠤⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢌⣭⣭⢭⣭⣭⡍⣭⠄⢤⡤⠀⢠⢤⡤⣤⡤⣤⣬⡄⢩⡤⢣⠁⡤⣤⠤⣬⢭⡬⣭⢬⡬⣿⢛⣤⢾⣿⢯⡭⣤⡬⣥⠤⡤⣤⢤⣤⣄⣤⣤⣤⣍⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠠⠿⠤⠾⠥⠤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⡄⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡝⢧⢤⡤⣄⠀⢠⡤⣴⢀⡤⣤⢠⡬⣤⢛⣢⣤⣤⢤⡤⣤⢮⡭⣤⡞⢣⡥⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣰⢀⣿⠀⣿⢩⣏⣸⣏⡷⠆⣼⡛⢡⣿⣻⣸⡙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⠿⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠉⠽⣿⡮⢽⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣿⡉⠉⠙⠈⠀⡀ ⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣤⣠⣄⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⢻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣀⣈⣵⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⠇ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣽⣿⣿⣿⣷⠀⠀⠀⠈⣻⡇⢸⡿⡿⠀⣿⣿⣿⡿⠘⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⢮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⣯⣴⡈⠋⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⠿⢿⠿⠿⣿⡤⠀⠀⠀⢟⠁⠈⠕⠇⠀⢿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⢿⠖⠂⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⢶⣷⠾⢶⣾⠿⠾⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣟⣭⣑⢳⣿⡿⠉⠉⠻⠟⠛⣒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢽⡂⣸⣿⡆⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠿⠟⠋⠉⠉⠀⠀⢄⣤⣠⣶⣥⣀⣀⣀⡠ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠧⣤⠠⡈⠙⠛⠁⠀⢘⣿⣧⣭⣴⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠉⠻⠉⠉⠙⠋⠀ ⣠⣤⣀⠀⠀⠛⣿⣿⡟⠀⠁⠠⠀⡼⠧⠘⢻⣦⡀⢀⣴⣷⣟⣻⠿⡟⡟⢻⣄⠀⡀⡀⣻⠋⡁⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣶⣾⣿⣿⡁⠀⠀⠀⠀⠀⠀⠄⣾⣿⣿⣿⣿⣿⡿⠁⠐⡇⠠⠬⠘⣀⠫⣷⣿⢶⣟⡇⠀⢠⠤⠀⣠⣿⣯⣿⣿⣿⣯⣤⣈⠻⢿⣿⡿⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠿⣶⣿⣿⣧⣤⣿⣿⢿⡫⠋⠀⠒⠂⠀⠀⠀⠀⠛⣆⠙⣿⡉⡏⡇⠀⠸⣴⢠⣿⡟⣏⡟⢿⣿⣿⡟⢁⣾⣿⣿⢣⡟⣾⣷⣤⠀⠀⠀⠀⠀⠀⠀⢠⡴⡃⠤⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣭⣭⢭⣭⣭⡍⣭⠄⢤⡤⠀⢠⢤⡤⣤⡤⣤⣬⡄⢩⡤⢣⠁⡤⣤⠬⣬⢭⡬⣭⢬⡬⣿⢛⣤⢾⣿⢿⡭⣤⡤⣥⠤⡤⣤⢤⣤⣄⣤⣤⣤⣍⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠠⠿⠤⠾⠥⠤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⡅⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡝⢧⢤⡤⣄⠀⢠⡤⣦⢀⡤⣤⢠⡾⣤⢛⣢⣤⣤⢤⡤⣤⢮⡭⣤⡞⢡⡥⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣰⢀⣿⠀⣿⢩⣏⣸⣏⡷⠆⣼⡛⢡⣿⣻⣸⡙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⢠⣬⣷⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠿⣿⣿⣯⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠄⠀⠀⠀⠀⠘⠮⡿⡺⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀ ⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⣄⣄⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⢻⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⢀⣀⣡⣽⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⠈ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣼⣿⣿⣿⣿⠄⠀⠀⠈⣻⡇⢸⡿⣿⠀⣿⣿⣿⡿⠋⠈⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣿⣯⣅⡉⠋⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⠿⢿⠿⠿⣿⡤⠀⠀⠀⠙⠁⠨⠵⠏⠀⢛⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⠿⠆⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢴⣶⠾⢷⣾⠿⡷⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣿⢿⣟⣭⣑⢳⣿⡿⠉⠉⠻⠟⠟⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣀⣬⣿⡆⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡗⠿⠟⠋⠉⠉⠀⠀⢀⣤⣀⣶⣥⣄⣀⣀⡀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠿⠿⠿⠧⣤⢀⡀⠉⠛⠁⠀⠀⣿⣧⣮⣵⣶⡄⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⠉⠉⠉⠙⠋⠁ ⣠⣤⣀⠀⠀⠙⣿⣿⡿⠀⠈⠸⠄⠼⠿⠜⢙⣦⣀⣀⣴⣿⣝⣛⠿⡟⠟⢻⣄⠀⣀⠀⣻⠋⣁⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣾⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣾⣿⣿⣃⠀⠀⠀⠀⠄⠀⡄⢴⣿⣿⣿⣿⣿⡿⠃⠀⠇⠠⠤⠸⢂⢱⣿⣿⢷⣧⡇⠀⠰⠤⠀⣠⣿⣯⣧⣿⣿⣯⣤⣬⠻⢿⣿⡿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠻⣷⣿⣿⣧⣤⣽⣿⣿⡻⠋⠀⠐⠂⠀⠀⠀⠀⠙⡯⢹⣿⡈⡏⠇⠀⠸⢴⢠⣿⡟⣏⡏⢿⣿⣿⡟⢀⣼⣿⣿⢃⡟⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⠶⡃⠤⠶⠎⠁⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣭⢭⣭⣭⡍⣭⠄⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡄⢫⡤⠣⠁⡤⣤⠬⣬⢭⡬⣭⢬⡤⣿⢛⣶⢾⣿⢯⡭⣤⡤⣭⠦⡤⣤⢤⣤⣄⣤⣤⣤⣌⡥⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⣇⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡝⢧⢤⡤⣄⠀⢠⡤⣦⢀⡤⣤⢠⡮⣤⢛⢢⣤⣤⢤⡤⣤⢬⡭⣴⡞⢡⡥⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣰⢀⣿⠀⣿⢩⣏⣸⣏⡷⠆⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⠀⠀⠀⠀⢠⣶⣾⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣛⣻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠉⢟⣿⣓⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡻⣟⣟⣿⣟⢿⣿⣿⣿⣿⣿⣿⣟⡉⢉⡀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⡤⣠⡄⠀⠀⠀⢸⣿⡇⢿⣿⣿⢻⣿⣿⣿⡿⢿⡿⠀⠀⠀⠀⠀⠀⢠⣭⣵⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣴⣿⣿⣿⣿⡧⠀⠀⠈⢹⡇⢸⡿⡿⠀⣿⣿⣿⣿⡛⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⣿⣖⡉⠋⠋⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⠿⢿⠿⠿⢿⣧⠄⠀⠀⠽⠁⠈⠁⠇⠀⢩⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⡿⠷⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣶⡾⢷⣾⡿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠟⣒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣥⣬⣽⠆⠠⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⢀⣠⣄⣲⣧⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⢛⠛⠓⣴⢤⡀⠉⠉⠁⠀⠀⣿⣿⣶⣭⣶⣄⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠛⠉⠋⠙⠉⠋⠀ ⢠⣤⣄⡀⠀⠉⣿⣿⡿⠀⠀⠐⠖⠼⠿⠎⢙⢦⣀⣀⣴⣿⣍⣛⠿⣾⢚⠻⣧⡀⣀⠀⣿⠋⡐⣿⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣾⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⡀⠀⠁⣀⡆⢼⣿⣿⣿⡿⣿⡿⠋⠀⠇⠠⠤⠐⢃⢹⣿⣿⢧⣯⡇⠀⠰⠦⠀⣰⣿⣯⣯⣿⣿⣭⣤⣬⠻⢿⣿⡿⣻⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠙⠻⣿⣿⣿⣷⣤⣽⣿⣻⠿⠋⠀⣐⡂⠀⠀⠀⠀⠉⡻⢻⣿⡈⡏⠇⠀⠸⣴⢠⣿⡟⣏⣏⢿⣿⣿⡟⢁⣼⣿⣿⢣⡟⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣶⡣⠤⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣭⢭⣭⣭⡍⣭⠗⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡌⢫⡤⠣⠁⡤⣤⠬⣬⢭⡬⣭⢬⡤⣿⢛⣶⢾⣿⢯⣭⣤⡬⣭⠦⡤⣤⢤⣤⣄⣤⣤⣤⣌⡥⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⣇⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡝⢧⢤⡤⣄⠀⢠⡤⣤⢀⡤⣤⢠⡮⣤⢻⢦⣬⣤⢤⡤⣤⢭⡭⣴⡞⢡⡥⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣰⢀⣿⠀⣿⢩⣏⣸⣏⡷⠆⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⠀⠀⠀⠀⠠⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠨⣿⣿⣟⡻⣽⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⢛⢽⣍⠙⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⣟⠿⣿⣿⣿⣿⣿⣿⠟⡉⠉⠁⠀⢀ ⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣄⣄⠀⠀⠀⢸⣿⡇⢿⣿⣿⠹⣿⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⣤⣖⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡗ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⣾⣿⣿⣿⣷⠀⠀⠈⣻⡇⢸⡿⣿⠀⣿⣿⣿⣟⡊⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⣯⣯⡞⠉⠉⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠿⢿⡿⠿⠿⣇⠄⠀⠈⢹⠁⢨⠵⠇⠀⢏⣿⣿⣿⣿⣿⡆⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⡿⠷⠀⠤ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣶⡾⢿⣶⡿⠷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣑⢳⣿⡿⠉⠉⠻⠟⠻⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣥⣬⣿⠆⠠⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⠀⣠⣤⣶⣧⣄⣀⣀⣀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⢛⢛⠛⣓⣲⢤⢀⠈⠉⠁⠀⠀⣿⣿⣶⣭⣶⣦⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠀ ⣠⣶⣤⣀⠀⢉⣿⣿⡿⠀⠀⠐⢟⠼⠿⠊⢈⣦⣀⣀⣴⣾⣭⣝⠿⠿⠫⠻⡧⡀⡄⠀⣿⠁⡄⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⡀⠀⢀⣀⡆⠴⣿⣿⣿⣿⣿⡿⠋⠀⠇⠰⠶⠀⢣⣸⣾⣿⢿⣷⡇⠀⠰⠖⠀⣰⣿⣧⣿⣿⣿⣽⣦⡬⢛⢿⣿⡿⣹⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠙⠻⣿⣿⣿⣷⣦⣼⣿⣻⠛⠋⢀⡐⠂⠀⠀⠀⠀⠉⣹⢹⣿⡌⡏⡇⠀⠘⢶⢠⣿⢟⣿⣏⢻⣿⣿⠟⢁⣾⣿⣿⢣⡟⣾⣿⣦⡄⠀⠀⠀⠀⠀⠀⢀⣖⠧⠴⠒⠛⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣭⢬⣭⣭⡍⣭⠗⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡌⢫⡤⠳⡀⡤⣤⠬⣬⢭⡬⣭⢬⡤⣿⢓⣶⢾⣿⢿⣭⣤⡬⣥⠦⡬⣤⢤⣤⣄⣤⣤⣤⣌⡥⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⣆⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡝⢧⢤⡤⣄⠀⢠⡴⣤⢀⡤⣤⢠⡮⣤⠻⢦⣬⣤⢤⡤⣤⢭⡥⣴⠞⢩⡥⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣸⢀⣿⠀⣿⢩⣏⣸⣟⡷⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠠⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠸⢿⣿⣟⣻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⣛⠭⠛⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⡏⡁⠈⠁⠀⠀ ⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣤⣄⣤⠀⠀⠀⢸⣿⡇⢿⣿⣿⢹⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠠⣬⣭⣼⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣴⣾⣿⣿⣿⣿⠀⠀⠈⣹⡇⢸⡿⣟⠀⣿⣿⣿⣟⡋⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⣿⣦⡉⠉⠉⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠿⠿⡿⠿⠿⣇⡤⠀⠀⢿⠀⠨⠿⠗⠀⢯⣿⣿⣿⣿⣿⠖⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣿⠷⠀⠠ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢶⡾⠿⣶⡾⠿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠛⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣗⣚⣿⠆⠀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⠀⣠⣄⣶⣧⣤⣠⣤⡤ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⡛⡛⡓⣲⢄⢄⠈⠉⠁⠀⠀⣿⣿⣶⣾⣷⣦⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠙⠉⠙⠉⠀ ⣴⣶⣤⣀⠀⢉⣿⣿⡿⠀⠀⠀⠮⠜⠛⠊⢉⣧⣀⣀⣴⣾⣯⣽⠟⠿⠩⠻⡧⡀⡤⠀⣻⠁⣄⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣿⣿⣿⣿⣥⣀⣀⣀⡀⢁⣀⡂⠼⣿⡽⣿⣿⣿⡟⠋⠀⠃⠐⠒⠐⢣⣰⣿⣿⢿⣿⡇⠀⢰⠖⠀⣰⣿⣷⣿⣿⣿⣿⣦⡬⢛⢿⣿⡿⣹⢏⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠙⠛⣿⣿⣿⣷⣶⣬⣿⣻⠿⠋⢀⣐⠁⠀⠀⠀⠀⠉⠹⢹⣿⣜⡯⡇⠀⠘⣾⣰⣿⢗⣯⣏⢻⣿⣿⠟⢀⣾⣿⣿⢣⣏⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢀⣞⠥⠐⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣬⣭⡍⣭⠕⢤⡤⠀⢠⢤⡴⣤⡤⣤⣤⡄⢫⡤⠳⠀⡤⣤⠬⣭⢭⡤⣭⢬⡤⣿⢛⣶⢾⣿⢯⡭⣤⡬⣭⠦⡬⣤⢤⣤⣄⣤⣤⣤⣌⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣤⡆⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⣆⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣄⠀⢠⡴⣤⢀⡦⣤⢠⡯⣤⠫⢦⣽⣤⢤⡤⣤⢭⡥⣴⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣸⢀⣿⠀⣿⢩⣏⣸⣟⡗⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠠⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢿⣿⣟⣟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢿⣿⡆⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡻⣟⣝⣿⣟⠿⣿⣿⣿⣿⣿⣿⣯⣄⠁⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣴⣄⣤⡀⠀⠀⢸⣿⡇⢿⣿⣿⠹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣤⣶⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠛ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣾⣿⣿⣿⣿⠄⠀⠈⣹⠇⢸⡟⡏⠀⣿⣿⣿⣿⣅⡉⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣿⣶⡋⠉⠉⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠿⠿⡿⠿⠿⣧⡤⠀⠀⢛⠀⠨⢅⠗⠀⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠄⢼⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⡿⠷⠂⠠ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢶⣶⣷⣶⣶⠿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠿⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⡟⢒⣻⠄⠀⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⠀⣤⣤⣶⣧⣄⣠⣠⡀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⡛⣛⡓⣶⢥⢄⠈⠉⠁⠀⠀⣿⣿⣶⣾⣷⣦⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠉⠉⠉⠉⠉⠀ ⣴⣶⣦⣀⡀⢈⣿⣿⡟⠀⠀⠈⠨⠚⠛⠊⢉⣧⣄⣀⣴⣾⣯⣭⠟⠿⠩⠻⡷⡠⣤⠀⣿⠁⣄⡿⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⠿⠿⢿⣿⣿⣿⣿⣿⣤⣀⣀⣀⡀⣀⣀⡂⠺⣿⣌⣿⣿⣿⠟⠁⠀⠇⠒⠒⠘⣡⣸⣿⣟⢿⣿⡇⠀⢰⠒⠀⣴⣿⣷⣿⣿⣿⣷⣦⡬⢛⣻⣿⡟⣿⢇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣶⣬⣿⣿⡟⠃⢀⠘⠁⠀⠀⠀⠀⠉⡹⢹⣿⣜⡏⡇⠀⠘⣞⣰⣿⢏⣯⣏⢻⣿⣿⠏⢠⣿⣿⣿⢱⣏⣿⣿⢷⡆⠀⠀⠀⠀⠀⠀⣠⣺⠅⠐⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣬⡍⣭⠝⢤⡤⠀⢠⢤⡼⣥⡤⣤⣤⡌⢫⡤⠱⠀⡤⣤⠤⣭⢭⡤⣭⢬⡤⣿⢛⣿⢿⣿⢯⡭⣤⡬⣭⠧⡭⣥⢤⣤⣄⣤⣤⣤⣌⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣴⡆⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⢆⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣄⠀⢠⡼⣤⢐⡦⣤⢠⡯⣤⠻⢤⣭⣤⢤⡤⣤⢭⡥⣴⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣸⢀⣿⠀⣿⢩⣏⣸⣟⡗⡃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⠔⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⣿⠿⢟⣹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠈⣿⣿⡨⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⣛⠿⣿⣿⣿⣿⣿⣿⣏⡌⠉⢀⢀⡀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⠆⣤⡀⠀⠀⢸⣿⡟⣿⣿⣿⢸⣿⣿⣿⣟⣛⣿⠀⠀⠀⠀⠀⢠⣬⣴⣴⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣽⣿⣾⣿⣿⠄⠀⠈⣽⠃⢺⡟⣟⠀⣿⣿⣿⣿⣍⣁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣷⣮⣍⠉⠉⠁ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠿⢿⣿⣿⣿⣿⠤⠀⠀⠌⠀⠘⠍⠅⠀⢽⣿⣿⣿⣿⡟⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⡿⠿⠷⠲⠆ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢶⣤⣼⣤⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠓⣃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⠟⠀⠚⠃⠐⢄⣀⠤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⠀⣠⣤⣶⣯⣤⣤⣤⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠙⢭⣭⣭⣽⢺⢢⡈⠒⠋⠀⢀⣾⣿⣿⣶⣯⣢⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠁⠀ ⣴⣷⣦⣤⣀⣠⣿⣿⠏⠀⠀⠈⠳⡚⠛⠁⢨⣷⠶⣄⣴⣾⣯⣭⠟⡞⠩⠹⢷⡤⡄⠈⣯⣀⣦⡿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠄⠀⠀⠀⠀ ⠛⠿⠿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣀⣠⣤⡅⣚⣿⣿⣿⣿⣿⠟⠁⠀⠃⠒⠒⠀⣡⣿⣿⣻⢻⣿⡇⠀⢘⠃⠀⣼⣿⣿⣾⣿⣿⣶⣶⠆⣛⣻⣿⡟⣿⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⡀⠌⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⡏⠇⠀⠘⡎⣼⣿⢣⣿⣏⢻⣿⣿⠃⣰⣿⣿⣿⣰⢧⣿⢿⣷⡆⠀⠀⠀⠀⠀⠀⣼⡿⠒⠚⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢤⡼⣥⡭⣤⣤⡭⢨⡤⠱⠀⡤⣤⠤⣭⢬⡥⣥⢤⡤⣽⢛⣿⢿⣿⢯⡭⣤⡬⣭⠵⡭⣥⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣶⡂⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⢂⢸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣄⠐⢰⡧⣤⢒⡤⣤⢨⡥⣤⠻⢤⣭⣤⢤⡤⣤⢭⡭⣼⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣏⡟⡃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠂⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⣿⣿⣛⡳⢾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢹⣿⣄⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡟⠿⣿⣿⣿⣿⣿⣿⣏⣬⡍⠀⢠⡀ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣶⠂⣦⡀⠀⠀⢸⣿⡟⣿⣿⣿⢹⣿⣿⣿⣟⣻⣟⠀⠀⠀⠀⠀⠠⣤⣧⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡷ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣔⣺⣿⣽⣿⣿⠀⠀⢈⣽⠁⢸⠟⡟⠀⣿⣿⣿⣿⣂⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣿⣍⣉⠉⠉⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠂⢿⣿⣿⣿⣿⣿⠀⠀⠀⡵⠀⠈⡙⠗⠀⢽⣿⣿⣿⣿⣟⠇⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⡿⠯⠠⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⢦⣀⣸⣄⣈⣹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠿⣃⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠹⠏⠱⠏⠐⢤⣀⠤⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⠀⣤⣤⣶⣷⣤⣀⣤⠄ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠛⢭⡍⣍⣽⢻⢢⡀⠒⠒⠁⢀⣾⣿⣿⣿⢿⣶⠀⠀⠀⠀⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠉⠉⠁⠀ ⣼⣿⣦⣤⣀⣠⣿⣿⠏⠀⠀⠈⠑⡚⠛⠁⢠⣻⡟⣇⣠⣾⣷⣿⠛⡏⡤⠙⢷⡄⡄⠀⣿⣀⣴⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠄⠀⠀⠀⠀ ⠛⠿⠿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣠⣤⣅⣼⣵⣿⣿⣿⣿⠟⠁⡀⠂⠚⠓⠈⣹⣿⡟⣛⢻⣿⡇⠀⢘⠃⠀⣼⣿⣿⢾⣿⣷⣶⣶⠆⣙⣻⣿⡏⣿⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣷⣽⡛⠁⠠⠈⠁⠀⠀⠀⠀⠀⢹⡏⣲⣾⡇⠇⠀⠘⡆⣼⣿⢫⣿⣏⢻⣿⡿⠃⣰⣿⣿⣿⣸⢧⡿⣿⣷⡆⠀⠀⠀⠀⠀⠀⣼⠿⠒⠚⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢬⡼⣥⡭⣤⣤⡅⢨⡤⠱⠀⡤⣤⠤⣭⢥⡥⣥⢤⡤⣽⢛⣿⢿⣿⢯⡭⣤⡬⣭⠵⡭⣥⢤⣤⣄⣤⣤⣤⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣶⡂⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⢂⢸⠏⠰⠟⠹⠇⠿⠹⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣄⠂⢺⡤⣴⢃⡤⣤⢨⡥⣤⠻⢤⣭⣤⢤⡤⣤⢭⡭⣼⠛⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣟⡟⡁⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⢠⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠘⣿⣿⣟⡘⣻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠐⢻⣿⡗⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⣟⠿⣿⣿⣿⣿⣿⣿⣯⣠⠄⠀⣤⣄ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⡶⠢⣄⡀⠀⠀⢸⣿⡇⣿⣿⣿⢸⣿⣿⣿⣿⢛⣛⠀⠀⠀⠀⠀⢠⣼⣧⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⡷ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡠⠛⣷⣰⣿⣷⠀⠀⢀⣽⠃⢸⡟⡿⠸⣿⣿⣿⣯⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢿⣿⣿⣿⣮⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⣿⣵⣍⠉⠁⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⢿⣿⣿⣿⣿⣿⠀⠀⠀⡚⠀⠘⡿⠋⠀⢽⣿⣿⣿⣿⡿⠃⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⡿⠟⠂⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⢄⠉⢉⡍⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠟⣃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠟⠃⠍⠐⢦⣀⠤⢄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⢠⣤⣴⣶⣷⣤⣠⣤⠄ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠚⢚⡯⣍⣿⢷⢄⡀⣢⣀⠂⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠀ ⣾⣿⣶⣤⣀⣰⣿⣿⠏⠀⠀⠀⠑⠚⠋⠁⢸⣻⡇⣇⣠⣾⣷⣾⠙⡏⡯⠹⢷⣤⡠⡂⣿⣀⣮⡿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠄⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣠⣤⣥⣿⣷⣿⣿⣿⣿⠟⠁⡀⠂⠘⠓⠘⣿⣿⡉⣿⢿⣿⡇⠀⢘⠃⠀⣼⣿⣿⣾⣿⣷⣾⣶⠆⣙⣻⣿⡟⣿⢣⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣿⣯⣼⡛⠁⡠⠈⠀⠀⠀⠀⠀⠏⣿⡄⢺⣮⡟⠇⠀⠘⡎⣼⣿⣫⣿⣎⢻⣿⡿⠃⣰⣿⣿⣿⣸⢧⡿⣿⣷⡆⠀⠀⠀⠀⠀⢀⣾⠟⠒⠚⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢬⡽⣥⡭⣤⣬⡅⢨⡤⠱⠀⡤⣤⠤⣭⢭⡥⣥⢤⡤⣽⢛⣿⢿⣿⢯⡭⣤⡬⣭⠵⡭⣥⢤⣤⣄⣤⣤⣤⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠽⠄⠰⠿⠤⠾⠥⣶⡂⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⢂⣸⠏⠰⠟⠹⠇⠿⠹⠼⢹⠯⠿⢸⣇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣄⠲⢫⡤⣼⢀⡤⣤⢨⡥⣤⠻⢤⣭⣤⢤⡤⣤⢯⡭⣽⠛⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣏⡟⡁⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⢿⣿⣛⠩⢽⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢝⣿⣍⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡻⣟⣟⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣤⡁⡀⡠⠀ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⡤⠤⣄⠀⠀⠀⢸⣿⡏⣿⣿⣿⢸⣿⣿⣿⡟⣛⣿⠀⠀⠀⠀⠀⢠⣴⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠿⣷⣰⣿⣧⠀⠀⢠⣿⠃⢸⡟⡟⠀⣿⣿⣿⣿⣠⣈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢿⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣿⣟⣋⠉⠁⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⢷⣿⣿⣿⣿⣿⠀⠀⠀⡼⠀⠘⠶⠇⠀⢾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⡿⠿⠿⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⠉⢛⡛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠷⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠈⠓⠜⠓⠀⠐⢦⣀⠤⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⢠⣤⣄⣶⣷⣤⣤⣤⡀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠐⢲⡪⣍⣿⢿⠀⠀⡦⡤⠂⢀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠁⠉⠉⠀ ⣾⣿⣶⣤⣀⣠⣿⡿⠋⠀⠀⠀⠑⠊⠋⠁⢸⡵⣇⡇⣠⣾⣷⣾⠛⡊⡈⠹⢗⡄⡄⠀⣿⣀⣞⡿⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣤⣤⣿⣿⣿⣿⢻⣿⣿⠟⠁⡀⠂⠙⠓⢸⣿⡇⠉⣟⢻⣿⡇⠀⢘⠃⢀⣾⣿⣿⢸⣿⣷⣾⣶⠆⣙⣻⣿⡏⡿⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣧⣼⡛⠁⡠⠈⠀⠀⠀⠀⢸⢻⣿⡀⢾⣼⡟⠇⠀⠘⡇⣼⣿⣫⣿⣏⢻⣿⡿⠃⣰⣿⣿⣿⣸⢷⡿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣾⠗⠐⠚⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡌⣭⠝⢤⡤⠀⢠⢬⡽⣥⡥⣬⣥⡅⢩⡤⠱⠀⡤⣤⠤⣭⢥⡤⣥⢤⡬⣽⢛⣿⢿⣿⢯⡭⣤⡬⣭⠥⡭⣥⢤⣤⣄⣤⣤⣬⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠽⠄⠰⠿⠤⠾⠥⣶⡂⠼⠇⠸⠯⠇⠿⠤⠸⠧⠴⢂⣸⠏⠰⠟⠹⠇⠿⠹⠼⢹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣔⠺⢣⡤⣥⢀⡤⣤⢨⡥⣤⠻⢤⣭⣤⢤⡤⣤⢯⡭⣼⠛⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⠰⢀⣿⠀⣿⢩⣏⣸⣏⡟⡁⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⡿⣻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⠻⢿⣟⡁⣺⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢹⣿⠀⢻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡟⠿⣿⣿⣿⣿⣿⣿⣋⢀⡁⠀⠠⠀ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⡤⢤⣀⠀⠀⠀⢸⣿⡏⢿⣿⣿⠸⣿⣿⣿⡟⡛⡛⠀⠀⠀⠀⠀⢠⣶⣿⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈⣿⣇⢰⣿⡆⠀⠀⠀⣿⠂⠸⡟⠟⠀⣿⣿⣿⣿⣄⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢿⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣿⣎⠋⠉⠁⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⣥⣾⣿⣿⣿⣧⠄⠀⠀⠩⠀⠘⠲⠀⠀⢻⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⠿⠿⠖⠐⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠛⠛⠒⢺⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠛⣊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠑⠀⣸⣇⠀⠐⢤⣀⠤⢀⡀⠀⠀⠀⠀⠀⣿⣿⢿⣯⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡗⠿⠟⠋⠉⠉⠀⠀⣤⣤⣀⣶⣷⣄⣀⣤⠄ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠐⠒⣫⣍⣽⣲⠀⠀⠏⠚⠄⠀⣼⣿⣿⣿⢿⣶⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⠁⠐⠂⠀⠀⠀⠀⠀⠀⠘⣛⠉⠉⠈⠈⠉⠉⠀ ⣼⣿⣶⣤⣀⣠⣿⡿⠋⠀⠀⠀⠑⠚⠛⣨⣴⣶⡼⡅⢠⣼⣷⣭⠙⡏⠌⠙⠗⡄⡄⠀⣿⣀⣜⡿⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡡⠀⠀⠀⠀⠀ ⠛⠿⠿⢿⣿⣿⣿⣶⣶⣤⣤⣤⣴⣦⣤⣿⣿⣿⠟⣹⣿⢿⠟⠁⠀⠂⠚⢳⣿⣷⡅⠁⠿⢻⣿⡇⠀⢘⠃⠀⣼⣿⣿⢸⣿⣿⣶⣶⠌⢙⣻⣿⡟⣿⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠹⠿⢿⣿⣿⣶⣶⣿⣽⡛⠁⠀⠈⠀⠀⠀⢸⠿⡇⡼⡀⢲⣼⡇⠇⠀⠘⡆⣼⣿⢫⣿⣎⢻⣿⣿⠃⣠⣿⣿⣿⣸⢧⣿⣿⢦⡀⠀⠀⠀⠀⠀⢠⣾⠥⠐⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢬⡼⣥⡤⣥⣤⡅⢨⡥⠱⠀⡤⣤⠤⣭⢤⡤⣥⢤⡬⣽⢛⣿⢿⣿⢯⡭⣤⡬⣭⠥⡭⣤⢤⣤⣄⣤⣤⣬⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣶⡂⠼⠇⠸⠯⠇⠿⠤⠸⠧⠴⠂⢸⠏⠰⠟⠹⠇⠿⠹⠼⢹⠯⠿⣸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣴⠇⢠⡧⣤⢀⡤⣤⢨⡥⣤⠻⢤⣭⣤⢤⡤⣤⢭⡭⣼⠛⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣏⡟⡃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⣾⣿⣿⣿⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⢛⣿⣟⣽⣶⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠐⢺⣿⣌⢩⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣿⣍⢬⠄⠈⢀⡀ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⡤⢤⣀⠀⠀⠀⢸⣿⡇⢿⣿⣿⠈⣿⣿⣿⣿⢛⣛⠀⠀⠀⠀⠀⠀⣼⣿⣵⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣖ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈⣿⣇⢰⣿⡆⠀⠀⠀⣼⡇⢸⡟⢿⠀⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⣷⣤⡋⠉⠉⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⣥⣾⣿⣿⣿⣇⠄⠀⠀⠭⠀⠀⡈⠓⠀⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⡿⠿⠆⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠛⠛⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣟⣽⣱⢳⣿⡿⠉⠉⠻⠟⠛⣂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠑⠀⣼⣇⠀⠐⢤⣀⠤⣀⡀⠀⠀⠀⠀⠀⣿⣿⣏⣯⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⣤⣤⣄⣶⣧⣄⣀⣤⡀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠒⡫⣍⣽⢺⠀⠀⠄⠹⠄⠀⣼⣿⣿⣿⢿⣶⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⠉⠉⠉⠉⠉⠉⠀ ⣼⣿⣶⣤⣀⣠⣿⠿⠋⠀⠀⠀⠑⠚⠛⣦⣾⣶⣾⡧⢀⣼⣧⣭⠟⡏⡨⠉⠗⡄⠄⠀⣿⣀⣎⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣡⠀⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣶⣦⣤⡿⠿⢿⣛⣸⣿⣿⠟⠁⠠⠀⠘⢺⣾⣷⡅⠀⡋⢻⣿⡇⠀⢘⠂⠀⣼⣿⣷⣾⣿⣿⣷⣶⠆⢙⣻⣿⡟⣿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⠿⢿⣿⣷⣶⣶⣭⣽⡋⠁⠀⠈⠀⠀⠀⢸⢹⡆⡼⡀⢾⣼⡏⡇⠀⠘⡎⣸⣿⢧⣿⣏⢻⣿⣿⠃⣠⣿⣿⣿⣱⢧⡿⣿⢄⡀⠀⠀⠀⠀⠀⢠⣶⠤⠰⠲⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢬⡼⣥⡤⣤⣤⡅⢨⡤⠱⠀⡤⣤⠤⣭⢤⡥⣥⢤⡤⣽⢛⣿⢿⣿⢯⡭⣤⡬⣭⠧⡭⣤⢤⣤⣄⣤⣤⣭⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣴⡆⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⠂⢸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣴⠂⢠⡦⣤⢀⡤⣤⢨⡥⣤⠻⢤⣭⣤⢤⡤⣤⢭⡥⣼⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣟⡟⡃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠟⣿⣿⣿⢾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣻⣿⣿⢻⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠘⢻⣿⣏⣨⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⣯⡉⠑⠒⢀⡄ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⡤⢤⣀⠀⠀⠀⢸⣿⡇⢿⣿⣿⠘⣿⣿⣿⣿⣛⡛⠀⠀⠀⠀⠀⢀⣼⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⠷⣿⣿⣿⣷ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⢿⣇⢰⣿⡆⠀⠀⠀⢸⡇⢸⡟⡿⠀⢿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢿⣿⣿⣿⣾⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⣿⣷⣏⠉⠉⠁ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⣵⣶⣿⣿⣿⣧⠄⠀⠀⡉⠁⠈⠒⢂⠀⢬⣿⣿⣿⣿⣟⠗⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⣽⣿⣶⣄⢾⣿⣿⣿⣿⣿⠿⠿⠆⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠛⠓⠒⢺⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠛⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠑⠂⢼⣧⠄⠐⢤⣀⠤⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⣤⣤⣤⣶⣷⣄⣀⣤⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠒⡫⣍⣽⢪⠀⠐⢴⡹⠄⠀⣼⣿⣿⣿⢿⣖⡀⠀⠀⠀⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣛⠉⡃⠉⠉⠉⠉⠀ ⣼⣿⣶⣤⣀⣠⣿⠿⠋⠀⠀⠀⠑⠚⠛⣷⣾⣿⣿⡷⢀⣼⣯⣭⠟⡏⠊⠉⠗⡄⡄⠀⣽⣁⣄⡿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣾⣧⣤⡿⠻⠿⣭⣼⣿⣿⠟⠁⠀⠂⠘⢳⣿⣿⡅⠀⡯⢳⣿⣇⠀⢘⠓⠀⣼⣿⣷⣿⣿⣿⣶⣶⡤⢙⣻⣿⡟⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣶⣶⣽⡫⠁⠀⠈⠁⠀⠀⢸⠿⡇⡸⡄⢺⣌⡇⠇⠀⠈⢾⣸⣿⢧⣷⣯⢻⣿⣿⠏⣠⣿⣿⣿⣱⣏⣿⢯⣀⠀⠀⠀⠀⠀⠀⢠⣶⠤⠴⠶⠿⠍⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢬⡼⣥⡤⣥⣤⡝⢨⡥⠑⠀⡤⣤⠤⣭⢤⡤⣥⢤⡤⣽⢛⣿⢿⣿⢯⡭⣤⡬⣭⠥⡭⣤⢤⣤⣄⣤⣤⣭⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣴⡆⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⠆⢸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣴⠂⢠⡦⣤⢀⡤⣤⢨⡧⣤⠻⢢⣭⣤⢤⡤⣤⢽⡭⣼⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣏⡟⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⢿⣿⣯⢼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢼⣿⣗⣚⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⣍⣋⣙⣁⣐⠀ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣤⡤⠤⣀⠀⠀⠀⠀⣿⡇⢸⣿⣿⠈⣿⣿⣿⣟⣛⣿⠁⠀⠀⠀⠀⢠⣤⣽⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⢿⣇⣰⣿⣇⠀⠀⠀⢹⠇⠸⡟⣻⠀⣿⣿⣿⣿⣥⣈⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣾⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⣿⣖⣉⠉⠁⠁ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⢷⣶⣿⣿⣿⣧⠄⠀⠀⠾⠁⠈⠔⠘⠀⠨⣿⣿⣿⣿⡟⠖⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⠿⠿⠯⠄⠐ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠄⡀⠙⠛⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠓⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠂⢸⠧⡄⠐⢦⣀⠤⣀⡀⠀⠀⠀⠀⠀⣿⣿⣯⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⣤⣤⣤⣶⣥⣄⣀⣤⡄ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠒⡪⡭⣽⣚⡄⠐⢜⡘⠆⠀⣼⣿⣿⣿⢿⣗⡀⠀⠀⠀⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⠡⠄⠀⠀⠀⠀⠀⠀⠀⢹⣟⠉⠉⠋⠉⠉⠉⠀ ⣼⣿⣶⣤⣀⣠⣿⡿⠋⠂⠀⠀⠑⠚⠛⣾⣿⣿⣿⡗⢀⣼⣯⣭⠝⡋⢸⠉⠟⡄⡄⠀⣿⡀⡄⡿⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⠀⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⣿⣷⣶⣤⣤⣴⣾⣧⣤⡟⠛⠻⢯⣴⣿⣿⠗⠁⠀⠂⠐⢒⣷⣿⣝⠀⠻⢱⣷⣇⠀⢘⠒⠀⣼⣟⣷⣧⣿⣿⣷⣶⡤⢙⣻⣿⡟⣽⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠹⢿⣿⣿⣿⣿⣶⣤⣽⡫⠃⠀⠈⠁⠀⠀⢀⡏⡇⢸⡄⢀⣄⣟⡏⠀⠘⢾⣰⣿⢏⣧⢇⠻⣿⣿⠋⢠⣿⣿⣿⢡⣏⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣴⠤⠤⠶⠶⠏⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡌⣭⠝⢤⡤⠀⢠⢤⡼⣧⡤⣤⣤⡍⢨⡤⠹⠀⡤⣤⠤⣭⢤⡤⣭⢤⡤⣿⢛⣿⢿⣿⢯⡭⣤⡬⣯⠥⡬⣤⢤⣤⣄⣤⣤⣭⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⢴⡆⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⠆⢸⠏⠰⠟⠹⠇⠿⠽⠼⣹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣴⠆⢠⡤⣤⢀⡤⣤⢨⡧⣤⠳⢢⣭⣤⢤⡤⣤⢯⡭⣬⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣟⡟⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⢿⣿⣛⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⢾⣿⣷⠽⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⣛⠿⣿⣿⣿⣿⣿⣿⣟⠿⣍⣀⣀⣄ ⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⡤⠤⣄⠀⠀⠀⠀⣿⡏⢹⣿⣿⠃⣿⣿⣿⣿⢛⣛⠀⠀⠀⠀⠀⢠⣤⣴⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡷ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠⠿⣧⣰⣿⣧⠀⠀⠀⣹⡇⠸⡟⠻⠀⣿⣿⣿⣿⣅⣉⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⢮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣿⣥⡩⠉⠙⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢶⣿⣿⣿⣿⣧⠀⠀⠀⠊⠃⠀⠐⢄⠀⠈⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⡿⠿⠄⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⡈⠉⢙⡋⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠟⠛⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠈⠒⢸⢷⡄⠐⢦⣀⠤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⣤⣤⣴⣦⣷⣄⣀⣀⡄ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠐⠒⡪⠭⣽⢪⠀⠐⢄⣊⠇⠀⣼⣿⣿⣷⢿⣗⡀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠛⠋⠈⠉⠉⠉⠁ ⣼⣷⣶⣤⣀⣠⣿⡿⠋⠀⠀⠀⠙⠞⠛⣦⣾⣿⣿⣟⢄⣼⣯⣭⠟⡚⡐⠉⠗⡄⣤⠀⣿⡁⡄⡿⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣉⠀⠀⠀⠀⠀ ⠛⠛⠿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣶⣧⣤⡿⠛⠿⢯⣥⣿⣯⡝⠁⠀⠂⠐⢒⣷⣿⣅⠀⠻⢳⣷⣧⠀⢐⠒⠀⣼⣟⣧⡇⣿⣿⣷⣶⡤⢙⣻⣿⡿⣹⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠹⢿⣿⣿⣷⣷⣶⣴⣽⡫⠋⠀⠀⠁⠀⠀⢀⡟⡇⠸⡄⢀⡄⡯⠋⠀⠘⢺⣰⣿⢇⣧⢇⠻⣿⣿⠟⢠⣾⣿⣿⢣⡟⣾⣧⠀⠀⠀⠀⠀⠀⠀⢠⣴⡀⠤⡴⠶⣊⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢤⡼⣧⡤⣤⣤⡝⢨⡤⠙⡄⡤⣤⠤⣭⢤⡤⣭⢤⡤⣯⢛⣿⢿⣿⢯⡭⣤⡬⣭⠧⡬⣤⢤⣤⣄⣤⣤⣬⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣤⡆⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⠇⢸⠏⠰⠟⠹⠇⠿⠽⠼⡹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣴⠆⢠⡤⣤⢀⡤⣤⢠⡧⣤⠻⢢⣬⣤⢤⡤⣤⢮⡭⣬⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢰⢀⣿⠀⣿⢩⣏⣸⣟⡟⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢭⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣍⡽⣉⡀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⡤⠤⣄⠀⠀⠀⠀⣿⡟⢻⣿⣿⠃⣿⣿⣿⣿⣛⣛⠃⠀⠀⠀⠀⠀⢤⣴⣾⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠⢿⣷⣼⣿⣷⠀⠀⠀⢸⡇⠸⡟⠛⠀⣿⣿⣿⣿⣁⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣿⣿⣦⣊⠋⠉⠁ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⢻⣿⣿⣿⣿⣿⠀⠀⠀⠬⠁⠀⠦⢅⠀⠨⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⡿⢿⠾⠇⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠢⣎⠉⢉⡍⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠟⠛⣂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠈⠉⠼⢿⡭⠀⢤⣀⠤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⣤⣤⣤⣦⣷⣆⣀⣠⡄ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠐⠖⠯⡭⣽⣖⠄⠀⢦⡆⠇⠀⣸⣿⣿⣷⢿⣗⡀⠀⠀⠀⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡉⠉⠉⠉⠉⠉⠁ ⣼⣶⣶⣤⣀⣠⣿⡿⠏⠀⠀⠀⠑⠜⠛⣢⣶⣿⣶⣟⢄⣼⣯⣭⠟⡛⡸⠉⡷⡄⠄⠀⣽⡁⡠⡿⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣚⠀⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣴⣦⣤⡽⠿⠿⠯⣅⣿⣯⡽⠋⠀⠅⠐⢲⣶⣿⣇⠀⢻⢳⣷⣧⠀⢐⠖⠀⣰⣿⣷⡇⣿⣿⣷⣶⡤⢙⣻⣿⡿⣹⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⢿⣿⣿⣷⣶⣶⣭⣽⡟⠋⠀⠀⠁⠀⠀⢸⢿⡇⠸⡄⢐⣄⣿⡏⠀⠘⢺⣰⣿⢇⣿⢧⠻⣿⣿⠟⢀⣾⣿⣿⢇⡟⣾⣇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠠⠤⠶⡖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢤⡼⣭⡤⣤⣤⡝⢨⡤⠙⡄⡤⣤⠤⣭⢤⡤⣭⢤⡤⣿⢛⣿⢿⣿⢯⡭⣤⡤⣭⠤⡬⣤⢤⣤⣄⣤⣤⣬⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⢤⡆⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⡇⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢧⢤⡤⣴⠂⢠⡤⣤⢀⡤⣤⢠⡯⣤⠻⢢⣬⣤⢤⡤⣤⢭⡥⣤⠟⢩⡤⣄⣤⠤⣤⣄⢠⣤⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢸⢂⣿⠀⣿⢩⣏⣸⣟⡟⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⠿⣿⣟⣝⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿ ⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢿⣿⣟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡻⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣭⣝⣁⡠⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣴⣤⠤⣄⡀⠀⠀⠀⣿⡿⢹⣿⣿⡇⣿⣿⣿⣿⣛⣻⠇⠀⠀⠀⠀⠀⣠⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⣿ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡠⢚⣿⣤⣿⣷⠀⠀⠀⢨⡏⠈⡿⠛⠁⢿⣿⣿⣿⣣⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣾⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⣿⣦⡍⢹⠋⠁ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠻⣿⣿⣿⣿⣿⠀⠀⠀⠐⠃⠀⠊⠑⠀⠨⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣿⢾⠆⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠲⢯⡉⢉⣍⠉⠹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣻⣿⣿⣿⡗⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠻⣂⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠉⠙⣛⣉⠁⢄⣀⠤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⣤⣤⣤⣆⣷⣦⣀⣠⣀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠙⠫⡯⡍⣽⢆⠀⠀⢦⡇⡉⠀⣸⣿⣿⣶⢿⣶⡀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⡉⡋⠉⠋⠛⠋⠁ ⣴⣷⣶⣤⣀⣠⣿⡿⠟⠀⠀⠀⠙⠞⠛⢊⣤⣶⣶⣾⢄⣼⣯⣭⠟⡘⣘⠉⠷⡄⢤⠀⢽⡁⣀⣽⠇⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀ ⠛⠛⠿⢿⣿⣿⣿⣷⣶⣤⣤⣄⣤⣤⣤⣽⡿⠿⣿⣛⣸⣿⡿⠋⠀⠄⠐⢲⣶⣿⡝⠀⢺⠻⣿⣿⠀⢐⡒⠀⣰⣿⣷⡇⣿⣿⣿⣶⡤⢙⣛⣿⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠙⢿⣿⣿⣿⣶⣶⣴⣽⡟⠋⠀⠐⠁⠀⠀⢸⢻⡇⠸⡄⠀⣄⣿⠏⠀⠘⢺⢠⣿⣟⣿⢧⠻⣿⣿⠟⢀⣼⣿⣿⢇⡿⣾⣷⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣤⢴⣖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢤⡼⣭⡤⣤⣤⡌⢨⡤⠙⡄⡤⣤⠤⣭⢤⡤⣭⢤⡤⣽⢛⣿⢿⣿⢯⡭⣤⡤⣭⠦⡬⣥⢤⣤⣄⣤⣤⣬⣍⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⡇⠸⠏⠰⠟⠹⠇⠿⠽⠼⡹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢯⢤⡤⣤⠀⢠⡤⣤⢀⡤⣤⢠⡯⣤⠻⢢⣤⣤⢤⡤⣤⢭⡭⣤⠟⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⢸⢀⣿⠀⣿⢩⣏⣸⣟⡟⠃⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠫⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⡿⣿⣿⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⢙⢿⣿⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠅⢁⣀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣤⣤⠤⣄⡀⠀⠀⠀⣿⣿⠸⣿⣿⡇⣿⣿⣿⣿⣿⣻⡃⠀⠀⠀⠀⠀⣄⣥⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⢞⣿⣦⣿⣿⡄⠀⠀⢈⡿⠀⡿⠻⠅⢸⣿⣿⣿⣿⣈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣾⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⣿⣦⡌⠟⠋⠁ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠸⣿⣿⣿⣿⣿⡅⠀⠀⠘⠁⠀⢀⠄⠀⠈⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣿⠶⠆⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠲⢯⡉⢉⣭⠉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠻⣛⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠉⠙⠛⠉⠁⢄⣀⢄⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⣄⣤⣄⣦⣷⣄⣀⣀⣀ ⠀⠀⠀⠀⠀⢼⣿⣿⣿⡋⠛⠫⡭⡭⣽⢢⡄⠀⠢⡏⢹⠀⢸⣿⣷⣶⢿⣢⡀⠀⠀⠀⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡙⢝⠉⠉⠙⠛⠁ ⣴⣶⣶⣤⣀⣀⣾⣿⠟⠀⠀⠀⠑⠜⠛⠋⢀⣶⣤⣴⣇⣰⣯⣙⡻⡜⢘⠉⡷⡄⣤⠀⣼⡁⣠⣽⠇⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⣠⣤⣼⣿⣿⣿⠿⠋⣿⡹⠋⠀⠇⠘⢲⣶⣿⡌⠀⢹⠫⣿⣿⠀⠐⡖⠀⣰⣿⣿⡇⣿⣿⣿⣶⡤⠝⣛⣿⣿⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠙⢿⣿⣿⣿⣷⣦⣮⣿⣟⠋⠀⠐⠀⠀⠀⢹⢹⠁⠹⡄⠈⣆⣿⠻⠀⠀⢲⢠⣿⡟⣿⣣⠻⣿⣿⡟⢀⣼⣿⣿⣏⡾⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⢀⣤⣤⣖⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣤⡍⣭⠝⢤⡤⠀⢠⢤⡤⣥⡤⣤⣤⡜⢠⡥⠙⡄⡤⣤⠤⣬⢥⡤⣬⢤⡤⣽⢛⣿⢿⣿⢯⡭⣤⡤⣭⠶⡤⣤⢤⣤⣄⣤⣤⣤⣅⡥⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣤⡄⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⡇⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡇⠿⠀⠼⠋⠿⠸⠏⠇⠾⠻⠇⠿⠹⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢿⢤⡤⣤⠀⢠⡤⣤⢀⡤⣤⢠⡭⣤⠻⢧⣤⣤⢤⡤⣤⢤⡭⣤⡉⢡⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣸⣂⣿⠀⣿⢩⣏⣸⣟⡟⠂⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠊⣿⣿⣿⣯⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣭⣿⣿⣿⡷⠀⠀⠀⠀⠀⠨⢿⣿⡝⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣝⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⡏⢩⡛⠉⠀ ⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⠤⢄⠀⠀⠀⠀⣾⣿⠸⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣭⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⢿⣶⣾⣦ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⢝⣿⣧⣿⣿⡄⠀⠀⢈⣿⠀⣿⠛⠇⢸⣿⣿⣿⣟⡙⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡻⣿⣿⡝⠋⢿⣿⣿⣿⣿⣇⣘⠛⠛⠏ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⠸⣿⣿⣿⣿⣿⡇⠀⠀⠐⠆⠀⠠⠱⠀⠈⢹⣿⣿⣿⣿⡷⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣿⣶⠀⡀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠲⢾⣉⠉⣩⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠛⣓⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠉⠹⠛⠉⠁⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣻⡁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡷⠾⠟⠋⠉⠉⠀⠀⢀⣠⣤⣂⣡⣆⠀⢀⣀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠩⢭⢟⡛⣿⢤⠀⠀⠻⢦⢴⠄⢸⣷⣶⣾⣵⣦⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⡷⠽⠛⠑⠂⠀⠀⠀⠀⠀⠀⠀⠈⢟⡛⠋⠛⠛⠛⠛⠋ ⣠⣶⣶⣤⣀⣀⣼⣿⡟⠀⠀⠀⠢⡱⠛⠒⠊⢢⠀⠘⡈⢠⣚⣛⡿⠹⢸⠋⡷⡀⡀⠀⢸⡏⢠⣸⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢐⠀⠀⠀⠀⠀ ⠛⠻⠿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⢀⣠⣤⣼⣿⣿⣿⡿⠿⢹⠟⠀⠅⠈⣶⣶⢳⡚⠀⠸⠻⣿⣾⠀⠠⠶⠂⢀⣿⣿⣾⣿⣿⣿⣷⣤⠝⡿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣯⣥⠀⠁⠀⠂⠀⠈⡏⡏⠉⠹⡄⠀⣆⣿⢺⠀⠀⢳⠀⣾⡿⣹⣳⠻⣿⣿⡿⠃⣰⣿⣿⡟⣼⣳⣿⣦⣄⠀⠀⠀⠀⠀⠀⣤⣆⣠⡤⠶⡎⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣬⡍⣭⠝⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡌⢠⡥⠙⡆⡤⣤⠤⣬⢥⡤⣬⢥⡤⣽⢛⣶⢾⣿⢿⡽⣥⡤⣭⠤⡤⣥⢤⣤⣄⣤⣤⣬⣍⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣄⣀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⡄⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢘⡏⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢿⢤⡤⣄⠀⢤⡤⣤⢀⡤⣤⢠⡬⣤⠺⢥⣤⣤⢤⡤⣤⢼⡥⣤⡈⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣸⣀⣿⠀⣿⢩⣏⣸⣟⡿⠂⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣟⡋⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠨⣾⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⡿⡟⢛⠟⠃⡐ ⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⠤⢄⠀⠀⠀⠀⢻⣿⠹⣿⣿⡇⢻⣿⣿⣿⠿⠿⠗⠀⠀⠀⠀⠀⡀⣩⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣝⣿⣦⣿⣷⡄⠀⠀⠈⣿⠀⣿⠻⠇⢸⣿⣿⣿⣿⡙⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡿⣿⣿⡝⠋⢿⣿⣿⣿⣿⣿⣽⠛⠛⠇ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢄⠸⣿⣿⣿⣿⣿⡇⠀⠀⠈⡃⠀⠩⠠⠀⠈⣹⣿⣿⣿⣿⣶⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣿⣦⡄⡀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠲⢾⣍⠉⣩⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠟⣓⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠙⠻⠛⠉⠉⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⣷⠿⠟⠛⠉⠉⠀⠀⠀⣠⣴⣂⣧⣄⡀⢀⣀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠿⣟⣛⡛⣿⠴⠀⠀⠻⢧⣠⡀⢸⣿⣴⣯⣶⣤⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠽⠙⠛⠛⠛⠋ ⣠⣶⣶⣄⣀⠀⣼⣿⡟⠀⠀⠀⠦⣲⠛⠒⠈⢄⠀⠈⠈⢡⣞⡻⢿⡹⢸⠛⣧⡀⣀⠀⢸⡏⢠⣸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣿⣿⣿⣿⣤⣄⣀⣀⣀⢀⣀⣐⣰⣶⣷⣶⣿⢎⢻⠟⠁⠆⠛⣶⣶⢣⡐⠀⢸⠿⣿⢺⠀⠀⠶⠀⢀⣾⣿⣧⣿⣿⣿⣧⣤⡙⠿⣿⣿⢿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣟⣋⠘⠃⠠⠂⠀⠀⡏⡟⠉⢹⡀⠈⣄⣿⢸⠀⠀⢳⠀⣼⡿⣻⣿⠻⣿⣿⡿⠃⣰⣿⣿⡟⣸⣱⣿⣷⡆⠀⠀⠀⠀⠀⠀⣴⡂⠠⠶⠞⠭⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣤⣬⡍⣭⠝⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡤⢠⡥⠙⡄⡤⣤⠤⣬⢭⡤⣬⢥⡤⣽⢛⣶⢶⣿⢿⡭⣥⡤⣯⠤⡤⣥⢤⣤⣄⣤⣤⣬⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣄⣀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⡄⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⠏⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢿⢤⡤⣄⠀⢤⡤⣤⢀⡤⣤⢠⡬⣥⠹⢧⣤⣤⢤⡤⣤⢤⡭⣦⡘⢩⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠌⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣸⣄⣿⠀⣿⢩⣏⣸⣟⡷⠆⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣇⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠨⢿⣿⣿⣍⣹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⣻⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣗⣟⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠁⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⠤⣀⠀⠀⠀⠀⢻⣿⠀⣿⣿⡇⢻⣿⣿⣿⡿⢿⠏⠀⠀⠀⠀⠀⠀⣈⣽⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣞ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣽⣷⣦⣿⣷⡄⠀⠀⠈⣿⠀⣿⠿⡇⢸⣿⣿⣿⣏⠙⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣿⣿⣯⡁⠿⠛⠉ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢄⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠋⠈⠀⠘⢹⣿⣿⣿⣿⡶⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣮⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣷⣦⡄⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢢⢶⣍⢉⣩⡉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣷⣿⣳⣿⣿⣿⣿⢿⣿⣽⣱⢳⣿⡿⠉⠉⠻⠟⠻⣛⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢙⣻⡛⠋⠉⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣽⡃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⣷⠾⠟⠛⠉⠉⠀⠀⠀⢠⣴⠂⣑⣀⠀⢀⡀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢛⣛⡛⡛⣿⠀⠀⠀⠻⠷⠠⠀⢸⣯⣮⣭⣶⢄⠀⠀⠀⠀⢸⣿⣷⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⡷⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢛⠛⠛⠛⠛⠛ ⢠⣶⣦⣄⡀⠀⣸⣿⡟⠀⠀⠀⢮⣰⠛⠂⠘⢄⠀⠈⡏⣧⡘⠿⢿⡙⠸⠛⣦⡀⣀⠀⢸⡏⢡⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠀⠀⠀⠀⠀ ⠿⠿⢿⣿⣿⣿⣿⣿⣤⣀⣀⣀⠀⢁⣀⣐⢀⣮⣷⣤⡷⡟⢋⠟⠁⠀⠂⣤⣷⢣⡀⠀⢸⠷⣿⢼⠀⠠⠦⠀⢀⣾⣿⡏⣿⣿⣿⣥⣄⡙⠿⣿⣿⢟⡿⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠃⠠⠀⠀⠈⡟⡇⠉⢱⡀⠈⡄⣿⢾⠀⠀⢧⠀⣼⡿⣻⣣⠻⣿⣿⡿⠋⣰⣯⣿⡟⡼⣴⡿⣶⡇⠀⠀⠀⠀⠀⢀⣶⡋⠠⠶⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣤⢤⣬⣭⡍⣭⠝⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡥⢠⡥⠹⡄⡤⣤⠤⣤⢭⡤⣬⢤⡤⣽⢛⣦⢶⣿⢭⡽⣥⡤⣭⠥⡭⣥⢤⣤⣄⣤⣤⣬⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣄⣀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⡄⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⠇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡌⢿⢤⡤⣄⠀⢤⡤⣤⢀⡤⣤⢠⡴⣥⠹⢣⣤⣤⢤⡤⣤⢤⡤⣷⡞⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣸⣄⣿⠀⣿⢩⣏⣸⣏⡷⠅⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣇⠀⠀⠀⠀⢀⢶⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠰⣿⣿⣿⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⠊⣼⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⡿⡻⡿⠋⠁ ⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣤⠄⣀⠀⠀⠀⠀⣿⣿⠓⣿⣿⡏⣿⣿⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣶⣦⣴⣦⡀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣽⣷⣶⣿⣷⡀⠀⠀⠘⣿⠀⣿⢿⡇⢸⣿⣿⣿⡏⠙⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢭⣿⣿⣿⣮⣿⣿⣟⡛⡛⣿⣿⡝⠋⢿⣿⣿⣿⣿⣋⡌⠿⠿⠫ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢄⢸⣿⣿⣿⣿⣿⡇⠀⠀⠰⠋⠀⠫⢀⠀⠘⢻⣿⣿⣿⣿⡶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣻⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣿⣷⣤⡀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢦⢾⣍⣉⣩⡉⠉⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠟⠛⣛⠌⠀⠈⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢙⣿⡛⠻⠉⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣻⣿⣷⣯⣷⡾⠟⠋⠉⠉⠀⠀⠀⢠⣔⠒⣓⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⢛⣛⡛⠛⣿⠘⡀⠀⠻⠶⠀⠀⢙⣯⣮⣭⣶⢄⠀⠀⠀⠀⢸⣿⣧⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠿⠛⠛⠳⠛⠛ ⢀⣶⣤⣀⡀⠀⣸⣿⡟⠀⠀⠈⢬⣰⠿⠄⠸⣄⠀⠐⡗⣦⠸⠿⣿⠟⠙⠻⣦⡀⠀⠀⢸⡏⠉⣹⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠿⠿⣿⣿⣿⣿⣿⣿⣤⣀⣀⡀⠀⢁⣀⣐⢐⣨⣦⣀⣧⡻⢟⡟⠁⠂⠢⣤⣵⢣⡁⠀⢸⠷⣿⣽⠀⠠⡤⠀⢀⣼⣿⡇⣿⣿⣿⣯⣀⡙⢿⣿⣿⢟⡿⣃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠉⠻⣿⣿⣿⣷⣿⣿⣿⣿⠗⠹⠋⠀⠄⠀⠘⡟⡇⠛⢣⠀⠀⡅⣿⢺⠀⠀⢥⠀⣸⡿⣿⣇⢻⣿⣿⡿⠋⣰⣷⣿⡟⡼⣵⣷⣦⡇⠀⠀⠀⠀⠀⢀⣴⣂⠠⠴⠿⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣬⢭⣭⣭⡍⣭⠗⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡥⢠⡥⠹⡄⡤⣤⠤⣤⢭⡤⣼⢤⡤⣽⢛⣤⢴⣯⢭⡽⣥⡤⣭⠤⡭⣤⢤⣤⣄⣤⣤⣬⣅⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⣄⣀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠄⡅⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⢸⡏⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡝⢿⢤⡤⣄⠀⢠⡤⣤⢀⡤⣤⢠⡴⣤⠙⢢⣤⣤⢤⡤⣤⢤⡤⣴⡞⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⢀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣰⣀⣿⠀⣿⢩⣏⣸⣏⡷⠅⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣇⠀⠀⠀⠀⠠⢴⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⡛⣟⣟⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠋⠉ ⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣿⣿⢽⣿⣿⡇⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⢩⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣶⢾⣗⣌⣠⣮⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣦ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢐⡿⣿⣶⣿⣦⡀⠀⠀⠙⣿⠈⣿⠿⡇⣿⣿⣿⣿⣗⠓⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⢽⣿⣿⣿⣮⣿⣿⣟⡛⡟⣿⣿⡝⠋⢿⣿⣿⣿⣿⡟⢹⠿⠿⠿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠈⠅⠀⠭⡞⠂⠘⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣯⣿⣿⣿⣯⣮⣿⣿⣿⡷⢽⣿⣶⣄⢾⣿⣿⣿⣿⣷⣷⣶⡄⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣦⢾⣍⠉⣩⡉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⡯⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣿⣻⢿⣿⣿⣿⣳⣿⣿⣿⣿⢿⣿⣭⣱⢳⣿⡿⠉⠉⠻⠟⠿⣛⠍⠛⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⢙⣻⡛⠻⢋⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⡃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣽⣮⣿⣿⣿⣿⡿⣿⣿⣷⣯⡷⠿⠟⠋⠉⠉⠀⠀⠀⢠⡤⢆⣡⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⣿⣿⠿⠿⣞⠀⡀⠀⠻⠥⠴⠀⢛⣥⣮⣵⣶⡄⠀⠀⠀⠀⣿⣿⣯⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⣿⣿⣿⣷⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠶⠿⠋ ⢀⣦⣤⣀⠀⠀⣠⣿⡟⠀⠀⠙⣝⣹⠿⠄⠹⣄⠀⢰⠒⣦⠾⢿⣿⡏⡟⢻⣆⠀⡀⠀⢸⠋⠉⣿⡄⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣿⣶⣿⣿⣄⡀⠀⠀⠈⢁⣀⡂⢨⢜⣦⣀⣧⡿⣿⠟⠀⠃⢂⣬⣼⢆⠩⠀⢿⣷⣟⣿⠀⢠⡤⠀⠀⣼⣯⡇⣿⣿⣿⣯⣀⡻⣿⣿⣿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠙⠻⣿⣾⣿⣧⣾⣿⣿⣿⡯⠻⠃⠀⠀⠀⠘⠟⡇⠛⣧⠀⠈⡈⣿⡿⠀⠰⢤⠀⢸⡿⣿⡇⢿⣿⣿⡿⠋⣰⣷⣿⡏⢯⣾⣦⡜⠀⠀⠀⠀⠀⠀⢀⣴⠂⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣤⣭⢭⣭⣭⡍⣭⠖⢤⡤⠀⢠⢤⡤⣤⡤⣤⣤⡄⢠⡥⢻⡁⡤⣤⠬⣤⢭⡤⣽⢤⡤⣽⢛⣤⢴⣯⢽⣿⣤⡬⣥⠭⡤⣭⢤⣤⣄⣤⣤⣬⣄⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠃⠿⠹⠄⠰⠿⠤⠾⠥⠄⠀⠼⠇⠸⠯⠇⠿⠤⠸⠧⠤⡁⠸⠏⠰⠟⠹⠇⠿⠽⠼⠹⠯⠿⣸⣇⠿⠀⠼⠋⠿⠸⠯⠇⠾⠻⠇⠿⠽⠄⠸⣝⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡀⠀⣤⡄⣠⠤⣤⢀⣤⠀⣤⢤⣠⣤⠀⠀⣠⡀⢤⡝⢧⢤⡤⣄⠀⣠⡤⣤⢀⡤⣤⢡⡴⣤⠛⢢⣤⣤⢤⡤⣤⢦⡤⣤⡟⢣⡤⣄⣤⠤⣤⣄⢠⣄⡤⢤⢤⡤⣠⢤⡀⣤⡀⡤⣤⢤⡤⣤⢤⣀⡤⡄⠀⠀ ⠀⠖⣾⣿⣏⢶⠎⠱⢿⣶⣶⡞⣿⣄⣿⠋⠉⠁⠀⡼⢻⣇⡏⠻⡏⣼⣧⠿⠀⣸⡿⣯⢿⣅⡿⣸⣯⡿⣰⣀⣿⠀⣿⢩⣏⣸⣟⡧⠁⣼⡛⢡⣿⣻⣸⠙⣿⢨⣛⡗⣾⡹⣇⡼⢣⡏⢷⢇⣿⣹⣴⡟⣿⣬⣻⠇⠀⠀ ䷩ 𝚕𝚒𝚗𝚎 2861 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_7/1/2022:_Krita_5.0.2_and_ChimeraOS_29⠀✐ Posted in News_Roundup at 4:30 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Server⠀➾ # ⚓ Kubernetes_is_Moving_on_From_Dockershim:_Commitments_and Next_Steps⠀⇛ Kubernetes is removing dockershim in the upcoming v1.24 release. We’re excited to reaffirm our community values by supporting open source container runtimes, enable a smaller kubelet, and increase engineering velocity for teams using Kubernetes. If you use Docker Engine as a Container Runtime for your Kubernetes cluster, get ready to migrate to 1.24! To check if you’re affected, refer to Check whether dockershim deprecation affects you. o § Audiocasts/Shows⠀➾ # ⚓ Hackaday_Podcast_150:_Blackberry_Runs_Out_Of_Juice,_NODE Has_Your_Pinouts,_Rats_Learn_DOOM,_And_2021_Is_Done_| Hackaday⠀⇛ Join Hackaday Editor-in-Chief Elliot Williams and Managing Editor Tom Nardi as they ring in the New Year with the first podcast episode of 2022. We get the bad news out early for those still thumbing away at their Blackberries, then pivot into some of the highlights from over the holidays such as the release of NODE’s The Pinouts Book and the discovery of a few expectation-defying OpenSCAD libraries. We’ll look at modifying a water cooler with Ghidra, and the incredible technology that let’s historians uncover the hidden history of paintings. Oh, and we’ll also talk about all the best and most important stories of the last 12 months. There’s a lot of ground to cover, so get comfortable. # ⚓ This_Week_in_Linux_179:_Lost_Torvalds_Talk_Found,_Maui Shell,_Krita,_Darktable,_OBS_Studio⠀⇛ On this episode of This Week in Linux, a Christmas Gift from Jon Maddog Hall of Linus talk from DECUS 1994, Krita 5.0, Darktable 3.8, OBS Studio 27.2 Flatpaks & Red Hat, OpenRGB 0.7, Firefox 95, GIMP 2.10.30, AppImage Pool: App Store for AppImages, Libadwaita 1.0, Enlightenment 0.25, Maui Shell: Convergent Desktop, Tails 4.25, Kali Linux 2021.4, Calculate Linux 22, Steam Winter Sale & Steam Awards, PS5 Controller as a Linux Touchpad! All that and much more on Your Weekly Source for Linux GNews! o § Kernel Space⠀➾ # ⚓ Linux_5.17_AArch64_Code_Has_SME_Preparations,_Adds_KCSAN Support_–_Phoronix⠀⇛ While the Linux 5.17 merge window hasn’t opened up yet, there have been a few early pull requests sent out this week ahead of this imminent next kernel cycle. One of those already sent out is the ARM64/ AArch64 CPU architecture code updates for Linux 5.17. Linux 5.17′s 64-bit ARM code has a few feature items at play and a lot of code cleaning / preparations for future kernel cycles. This pull is just about the architecture work and not the Arm platform/DT updates for new SoC and hardware support, which will be sent separately as a PR during the merge window. # ⚓ Linux_5.17_Picking_Up_Support_For_New_NVIDIA_Spectrum- 4_Network_ASIC_–_Phoronix⠀⇛ As part of the plethora of networking changes for Linux 5.17, NVIDIA is introducing support for Spectrum-4 networking ASICs. For Linux on the NVIDIA (Mellanox) Spectrum Open Ethernet Switches there is the MLXSW driver for supporting the Ethernet Switch ASICs. That Mellanox network driver has supported Spectrum, Spectrum-2, and Spectrum3- families of Ethernet switches while queued up now in time for Linux 5.17 is Spectrum- 4 support. With the latest NVIDIA Spectrum SN4000 series Ethernet switches being based on Spectrum-3, it doesn’t appear there is any Spectrum-4 hardware out yet in the marketplace. # ⚓ Linux_5.17_Random_Number_Generator_Seeing_Speed-Ups, Switching_From_SHA1_To_BLAKE2s_–_Phoronix⠀⇛ Ahead of the Linux 5.17 merge window officially opening next week, random (RNG) subsystem maintainer Jason Donenfeld has submitted an exciting batch of updates for this next kernel cycle. As covered at the end of December, Linux is replacing SHA1 usage with BLAKE2s as part of its entropy extractor code. The BLAKE2s code is not only more secure than SHA1 but also faster. This BLAKE2s usage was found to improve the entropy extraction by 131%. # ⚓ Intel_develops_an_exclusive_firmware_update_driver_for Linux_–_itsfoss.net⠀⇛ Intel is implementing a feature support for the motherboards that, at least for now, will be Linux exclusive, a detail that is not usually the norm in the hardware world, where Windows is the highest priority in almost 100% of cases, even for Intel, which is practically the manufacturer that best supports Linux. Being more specific, Intel has introduced a future Linux 5.17 driver called “pfr_update” that will make use of the specification Platform Firmware Runtime Update and Telemetry ACPI (PFRUT), which allows updating a BIOS or UEFI without the need to reboot. For now this feature will not reach Windows, but who doubts that this exclusivity aims to be ephemeral. It doesn’t take a lynx to realize that Intel’s priority of Linux over Windows is due to the use of PFRUT I know will focus on servers, where workloads often cannot be interrupted. The ACPI specification will allow BIOS / UEFI updates to be carried out on the fly, thus eliminating, at least on paper, a potential outage scenario. In addition, it also incorporates a controller to read telemetry data from the firmware in a standardized way. # ⚓ Linux_Hibernation_Documentation_–_Tookmund_–_A_place_for_my random_thoughts_about_software⠀⇛ Recently I’ve been curious about how hibernation works on Linux, as it’s an interesting interaction between hardware and software. There are some notes in the Arch wiki and the kernel documentation (as well as some kernel documentation on debugging hibernation and on sleep states more generally), and of course the ACPI Specification # § Graphics Stack⠀➾ # ⚓ Microsoft_Eyeing_OpenGL_Compute_+_GLES_3.1_For_Its Mesa_D3D12_Backend [Ed: This is about promoting Windows, Not Linux, but the headline does not tell you that. One needs to read the_comments to know what’s really going on here…]⠀⇛ o § Benchmarks⠀➾ # ⚓ AMD_Radeon_Open-Source_Linux_GPU_Driver_Performance:_2020 vs._2021⠀⇛ Across dozens of articles over the past year I have covered a variety of different open-source AMD Radeon Linux graphics driver optimizations from their kernel driver through their Mesa RadeonSI Gallium3D driver and the popular RADV Vulkan driver, among other interesting open-source AMD contributions. For those wondering what the cumulative gain was for 2021 from all these AMD graphics driver changes, here are some end-of-year 2020 vs. 2021 benchmarks across a number of different Linux games while testing on Vega, Navi, and Navi 2 graphics cards. Today’s article is summing up the overall impact of AMD’s 2021 Linux graphics driver optimizations. For reasonably looking at that cumulative impact the following software configurations were tested… o § Applications⠀➾ # ⚓ qBittorrent_4.4_Open-Source_BitTorrent_Client_Adds_an Official_AppImage,_Qt_6_Support⠀⇛ After more than half a year of development, qBittorrent 4.4 is finally and it’s the first stable release of popular BitTorrent client to offer a pre-compiled binary in the AppImage universal binary format for GNU/Linux distributions. The good news is that it’s now a lot easier to run qBittorrent on your favorite distro. Created on Ubuntu 20.04 LTS, the AppImage doesn’t require installation and uses the latest versions of the Qt 6, libtorrent, Boost, and OpenSSL libraries. # ⚓ mop_–_terminal-based_stock_market_tracker⠀⇛ A stock ticker is a report of the price of specific securities, updated continuously throughout the trading session by the various stock market exchanges. The term “tick” refers to a change in a security’s price from one trade to the next. A stock ticker displays these ticks, along with other relevant information, like trading volume, that investors and traders use to stay informed about current market conditions and the interest in that particular security. The ticker provides current information for certain stocks, including the ticker symbol (the one-to four-letter code that represents a particular stock), quantity traded (volume for each transaction), price, a green “up” arrow if the price is higher than the previous day’s closing value, a red “down” arrow if the price is lower, and the net price change (either as a monetary amount or percentage) from the previous day’s close. o § Instructionals/Technical⠀➾ # ⚓ 5_Best_Practices_for_Securing_SSH⠀⇛ Strictly following security best practices is the first step to cybersecurity. Although SSH is the industry standard for both security and efficacy for remote server access, as with any software, SSH is only as secure as configurations applied to the server and client configurations. In this article, we’ll explore five SSH best practices you should observe to boost the security of your infrastructure. # ⚓ VPN_as_a_Dev_Tool⠀⇛ Personally, I’ve started to use a VPN between my workstation, laptop, and mobile devices. I could imagine it starting to be useful for hybrid development – running some services locally and others in the cloud. Of course, this whole setup could be leapfrogged once we move to remote development. # ⚓ Toward_a_Best-of-Both-Worlds_Binary_Disassembler⠀⇛ Binary disassembly is surprisingly difficult. Many disassembly tasks (e.g., code/data disambiguation and function boundary detection) are undecidable and require meticulous heuristics and algorithms to cover the wide range of real-world binary semantics. An ideal disassembler has two key properties: (1) transparency, meaning that its underlying logic is accessible and interpretable, and (2) mutability, meaning that it permits ad hoc interaction and refinement. Unfortunately, despite the abundance of disassembly tools available today, none have both transparency and mutability. Most off-the-shelf disassemblers (e.g., objdump, Dyninst, McSema, and Angr) perform “run-and-done” disassembly, and while their underlying heuristics and algorithms are indeed open source, even the slightest of changes (e.g., toggling on a heuristic) requires a complete rebuild of the tool and regeneration of the disassembly. In contrast, popular commercial disassemblers like IDA Pro and Binary Ninja provide rich interfaces for user- written plugins, yet these tools are almost entirely proprietary, making it impossible to fully vet where their core heuristics and algorithms fall short. Thus, reverse engineers are left to choose between two classes of disassemblers: those full of ambiguity or those with zero flexibility. In this blog post, I introduce our vision for a best-of-both-worlds (transparent and mutable) platform for binary disassembly. Our approach was inspired by recent disassembly tools like ddisasm and d3re, which use the Soufflé Datalog engine. Dr. Disassembler uses Trail of Bits’ in-house incremental and differential Datalog engine, Dr. Lojekyll, to specify the disassembly process. Below, I describe how Dr. Disassembler’s relational view of disassembly is a step toward transparent, mutable disassembly—streamlining the integration of new heuristics, algorithms, and retroactive updates—without the need to perform de novo disassembly per every incremental update. # ⚓ How_to_add_users_to_Jira_boards⠀⇛ Jira is a popular task management tools used across multiple industries. It is exceptionally popular in IT and is built to be used with the Agile framework but if you know how to use and organize things in Jira, you can use it in almost any field. # ⚓ How_to_install_PrestoDB_with_Podman_–_NextGenTips⠀⇛ In this article, we are going to learn how to install PrestoDB with Podman. Presto is a high-performance, distributed SQL query engine for big data, its architecture allows users to query a variety of data sources such as Hadoop, AWS S3, Teradata, Cassandra, Kafka, etc. You can even query data from multiple sources within a single query. # ⚓ How_to_install_Proxmox_VE_on_Linux_|_FOSS_Linux⠀⇛ Proxmox virtual environment, popularly known as Proxmox VE, is an open-source server virtualization software based on Debian Linux in conjunction with RHEL kernel, which is modified to permit you to generate and set up new virtual machines for private servers and containers with unified storage for improved efficiency. This software offers two versions of virtualizations. The first is containers with LXC, and full virtualization with KVM comes as the second. Virtualization is the basis of cloud computing as it allows for more proficient usage of physical PC hardware. # ⚓ How_to_Install_VMware_Tools_(OpenVM_Tools)_on_Ubuntu_20.04 /_22.04_LTS_–_LinuxCapable⠀⇛ Sometimes you may want to install an Ubuntu desktop or server on a virtual machine. However, you may have realized that communication between the host and the VM machine doesn’t exist. Luckily, many distributions now carry the open-source VM tools that can be used for many of the most popular Virtual Machine products such as VMware. In the following small tutorial, you will learn how to install these tools on either Ubuntu 20.04 LTS Focal Fossa or Ubuntu 22.04 LTS Jammy Jellyfish server or desktop environment. # ⚓ How_to_Set_a_Custom_SSH_Warning_Banner_or_MOTD_in_Linux⠀⇛ SSH banner warnings are necessary when companies or organizations want to display a stern warning to discourage unauthorized parties from accessing a server. These warnings appear immediately before the password prompt, informing unauthorised users who are about to log in of the implications of doing so. Typically, these warnings represent legal consequences that unauthorised users may face if they continue to access the server. Follow this guide to see how you can set a custom warning banner. # ⚓ How_to_Set,_List_and_Remove_Environment_Variables_in Linux⠀⇛ Since this post shares cloud strategies with awesome people like you, naturally this post may contain affiliate links for products I use and love. If you click on those links and make a purchase, I’ll earn some coffee money which I promise to drink while creating more helpful content like this. # ⚓ How_to_Install_GIMP_(GNU_Image_Manipulation_Program)_on Linux_Mint_20_–_LinuxCapable⠀⇛ GIMP, better known as GNU Image Manipulation Program, is a free, open-source raster graphics editing software primarily used for image manipulation and image editing, transcoding between various image formats, free-form drawing, and many more specialized tasks. GIMP is released under GPL- 3.0-or-later license and is available for Linux, macOS, and Microsoft Windows. In the following tutorial, you will learn to install the GIMP application with Linux Mint 20 using three alternative methods. # ⚓ How_to_Install_Glances_System_Monitor_on_Ubuntu_22.04_LTS_– LinuxCapable⠀⇛ Glances System Monitor is free, an open-source command-line tool for process monitoring, system resources such as CPU, Disk I/O, File System, Load Average, Memory, Network Interfaces and processes. Glances are built with Python language. Glances support cross-platform monitoring, which can be used with a web-based interface. One of the excellent features Glances supports is setting thresholds in the program. You can set careful, warning, and critical in the configuration file, which will then relay information in colors that can show alerts to systems resources bottlenecks, system resources issues, and much more. Glances, by default, comes with a pre-set list of colors, but you can modify and add additional configs. The following tutorial will demonstrate how to install or enable and configure Glances System Monitor on Ubuntu 22.04 LTS Jammy Jellyfish Desktop or Server. # ⚓ How_to_Install_PostgreSQL_14_in_Fedora_Linux⠀⇛ Fedora Linux is a safe haven for most open-source Linux applications and projects. Most OS users prefer to use this RHEL-based Linux distribution as an ideal candidate for learning and mastering new skillsets through its rich catalogs of educational software. One such educational software is PostgreSQL, which is an open-source relational database management system (RDBMS) used by analytics, geospatial, mobile, web, and other enterprising applications as a primary data warehouse or data store. PostgreSQL is favored by such applications and projects footprints because of its luring attributes. They include its diversified extension functions, support for flexible full-text search, diverse indexing techniques, and its growing community support. Among this attribute list, the most important element is community support. It helps new and intermediate users understand the interpretation of PostgreSQL software functions and their implementation. # ⚓ How_to_Install_SQLite_3_on_Debian_11_Bullseye_– LinuxCapable⠀⇛ SQLite is a free, lightweight relational database management system (RDBMS) in a C library. SQLite is not a client-server database engine. Instead, it is embedded into the end program. Primarily all programming languages support SQLite, which how languages embed the program is with a file with .sqlite3/.sqlite/.DB extension. The software is a popular choice for local/client storage such as web browsers, Android devices, and much more. The list is quite extensive. In the following tutorial, you will learn how to install SQLite 3 along with Debian 11 Bullseye. # ⚓ How_To_Install_TeamViewer_on_Fedora_35_–_idroot⠀⇛ In this tutorial, we will show you how to install TeamViewer on Fedora 35. For those of you who didn’t know, TeamViewer is a powerful remote desktop and file-sharing application that works with most operating systems (Microsoft Windows, macOS) and mobile devices. With TeamViewer, you control another computer over the Internet or have someone else control your own computer. For example, solve problems on customers’ PCs or give you access to a PC that is not currently nearby. In order to commercialize the use of TeamViewer, you have to purchase a license. You can use it free for personal use only. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you the step-by-step installation of the TeamViewer remote desktop application on a Fedora 35. # ⚓ How_To_Install_XanMod_Kernel_on_Ubuntu_20.04_LTS_–_idroot⠀⇛ In this tutorial, we will show you how to install XanMod Kernel on Ubuntu 20.04 LTS. For those of you who didn’t know, XanMod is a custom-built kernel for Debian and Ubuntu operating systems that comes with a couple of tweaks for optimizing the performance. The real-time version is recommended for critical runtime applications such as Linux gaming eSports, streaming, live productions, and ultra-low latency enthusiasts. This article assumes you have at least basic knowledge of Linux, know how to use the shell, and most importantly, you host your site on your own VPS. The installation is quite simple and assumes you are running in the root account, if not you may need to add ‘sudo‘ to the commands to get root privileges. I will show you through the step-by- step installation of the XanMod Linux Kernel on Ubuntu 20.04 (Focal Fossa). You can follow the same instructions for Ubuntu 18.04, 16.04, and any other Debian-based distribution like Linux Mint. # ⚓ How_To_Use_Screen_Command_on_Linux_To_Manage_Terminals⠀⇛ The screen command is a terminal command that can play the role of the multiplexer. In other words, you can run screen commands on your terminal shell to keep applications live in the background, run packages as a daemon, and keep a session (SSH) live for a long time even if you’re disconnected. The screen command is helpful and handy for all system administrators and Linux power users. This multiplexer type tool is powerful to run shell commands between a server, console, and other machines. # ⚓ How_To_install_Flarum_Forum_software_on_Ubuntu_22.04_| 20.04⠀⇛ Do you want to host your own discussion forum software? Then here is the tutorial to install and configure Flarum on Ubuntu 20.04 Focal or Ubuntu 22.04 Jammy Jellyfish. Flarum is the combined successor of esoTalk and FluxBB forums. It is a newbie in the forums world but still one of the best forum interfaces along with a sleek and modern look. The user interface is simple, fast, and free from clutter and bloats. Flarum is built with PHP so it’s quick and easy to deploy. The interface is powered by Mithril, a performant JavaScript framework with a tiny footprint. Right now to installation this forum you need SSH access to the hosting server and install the composer. This forum is still in the beta stage so before using it for production you need to give it some time. But still, for your own experience, you can install and use it. After stable release, it can be proved the best alternative to the Discourse forum. # ⚓ Install_QBittorrent_4.4.0_On_Ubuntu_/_Linux_Mint_&_Fedora_| Tips_On_UNIX⠀⇛ This tutorial will be useful for beginners to install qBittorrent 4.4.0 on Ubuntu 20.04, Ubuntu 20.10, and Linux Mint 20.3, and Fedora 35 qBittorrent is one of the best open-source torrent clients with more features and lightweight and it is written on QT6. It is using the libtorrent-raster library, which means it will support all operating systems Windows, Linux, macOS, and FreeBSD. # ⚓ Install_Zeek_on_Debian_11_–_kifarunix.com⠀⇛ Follow through this tutorial to learn how to install Zeek on Debian 11. Zeek, formerly Bro IDS, is the world’s leading passive open source network security monitoring tool. Zeek is not an active security device, like a firewall or intrusion prevention system. Rather, Zeek sits on a “sensor”, a hardware, software, virtual, or cloud platform that quietly and unobtrusively observes network traffic. Zeek interprets what it sees and creates compact, high-fidelity transaction logs, file content, and fully customized output, suitable for manual review on disk or in a more analyst-friendly tool like a security and information event management (SIEM) system. # ⚓ Install_MongoDB_Compass_GUI_on_AlmaLinux_or_Rocky_Linux_8⠀⇛ MongoDB is a NoSQL database server with a command- line shell interface, however, to manage with GUI, we can install MongoDB Compass on Rocky Linux or AlmaLinux 8 using the terminal. It is a good alternative to the MongoDB shell for querying, aggregating, and analyzing databases. Unlike MySQL, MariaDB, and other SQL; MongoDB is a NoSQL document-oriented database. Relational database technologies use rows, columns, and tables to store data. This makes them rigid quickly, slowly, and nearly impossible to manage; just imagine Microsoft Excel. Compared to database systems like MySQL, the structure of the data is not determined per table, but per entry, which gives me greater flexibility. Its name comes from humongous. MongoDB is also one of the most popular databases among developers. # ⚓ Install_Libreoffice_7.2.5_On_Ubuntu_/_Linux_Mint_&_Fedora_| Tips_On_UNIX⠀⇛ This tutorial will be helpful for beginners to install LibreOffice 7.2.5 on Ubuntu 20.04 LTS, Ubuntu 21.10, LinuxMint 20.2, and Fedora 35. LibreOffice released the newer and 5th version in the 7 series as 7.2.5 and it comes with new features and bug fixes and program enhancements and all users are requested to update to this version as soon as possible. # ⚓ Setup_MailCow_Server_With_Debian_11⠀⇛ So, today in this tutorial we will learn to install the MailCow server with Debian11. MailCow is an open-source mailing script developed on top of Dovecot, Postfix, SoGo, and other open-source applications. In addition, it has a modern web- based user interface for administering users as well as the server. Refer to this link for other email service articles. # ⚓ Centos/RHEL_8_Set_Grub_password⠀⇛ So, this tutorial provides step-by-step instructions on recovering/reset lost or forgotten RHEL 8 / CentOS 8 Linux root administrative passwords. To first boot to the set GRUB password and usernames required. So that non-authorized users cannot modify the grub entry at the boot loader stage. Also, check setting up grub for Ubuntu. # ⚓ How_to_Make_GNOME_Shell_Look_Like_Unity_(‘Cos_Why_Not, Right?) ⠀⇛ Want to make GNOME Shell look like the Unity desktop? If you do, then this guide is for you. Just don’t thank me for what follows. A reader called Alwyn sent the whole run-through to me via the Tip Form, complete with screenshots. They said I could publish it if I found it interesting (which surprise: I did). Now, I’m uneasy publishing anything not written — typo’d? — by me (you may notice I’m the only regular author around here). There are a number of reasons for this but the chief one is that I can’t afford to pay for contributions. It’s just not fair to expect people to write for nothing. # ⚓ How_to_Install_CloudPanel_Control_Panel_on_Debian_10 Server⠀⇛ CloudPanel is an open-source and free server Control panel, optimal to use on command line Debian Linux servers to manage various web components, for system monitoring and other services like MySQL, NGINX, PHP-FPM, and Redis. Most of the time hosting services come with a popular WHM Cpanel, however, we have to pay an extra cost for that. Thus, those who have some knowledge of the Linux operating system and command line can use free CloudPanel on various VPS hosting including Public cloud platforms such as Amazon Web Services, Digital Ocean, or Google Cloud. The good thing is, this open-source Linux server control panel comes with extra functionalities to integrate properly with Public cloud services, aforementioned, to manage their various features. For example: # ⚓ How_to_install_ImageMagick_&_its_PHP_module_on_Debian_11 Server⠀⇛ Tutorial to learn the simple commands for installing ImageMagick on Debian 11 Bullseye server along with PHP-Imagick module to use for various web-based applications such as WordPress. ImageMagick is a free tool distributed under an open-source license. Using it various images can be converted, compared, or overlapped. Apart from that other functions such as cropping, enlarging, and reducing the photos are also there. ImageMagick can handle over 100 image formats. To use its functionality in PHP-based applications, the user has to install the Imagick PHP extension. ImageMagick itself provides the user interface for the most important basic functions. Even new users can easily understand and get along with the software. Special editing features are only available as command-line tools and are therefore somewhat more complicated to use. # ⚓ Install_build_essential_tools_on_Ubuntu_22.04_or_20.04_LTS Linux⠀⇛ To compile programs from their source code, we need some tools and libraries available through a single package called on Build essential on Ubuntu 20.04 | 22.04 |18.04 or Debian 11 | 10 base repository. Here we learn how to install it. Build essential is a name for a package that includes the GCC/g++ compilers and libraries and some other utilities required to compile software written in C and C++. The Gnu Compiler Collection, GCC for short, is a collection of compilers and offers a uniform interface for creating programs in C, C ++, Objective-C, Fortran, Ada, Assembler and Go. # ⚓ How_to_install_Nim_programming_language_on_Debian_11⠀⇛ Hello, dear readers. Today, you will learn how to install the Nim programming language on Debian 11. Nim is a programming language that has been inspired by Delphi. Therefore, it is a compiled language that focuses on efficiency, ease of reading source code and flexibility. Nim combines successful concepts from mature languages like Python, Ada and Modula. In addition to this, it is open source, so we can examine its source code. We could say that Nim is a new language that promises to incorporate improvements and alternatives to what already exists. For example, it can be integrated for backend functions with Python, C and others. o § Wine or Emulation⠀➾ # ⚓ Wine_7.0′s_Many_Features_From_Better_Theming_To_Improved HiDPI_To_New_Joystick_Driver⠀⇛ We are closing in on the release of Wine 7.0 as the annual stable feature release for this open-source software that allows running Windows games and applications under Linux, macOS, BSDs, and other platforms. Here is a recap of the many changes being introduced since last year’s Wine 6.0 milestone. Wine 7.0 has been seeing weekly release candidates and is expected for its formal release this month. In fact, it could be as soon as next week going off the project’s usual RC rhythm. o § Games⠀➾ # ⚓ Check_out_some_fresh_Haunted_Chocolatier_screenshots_| GamingOnLinux⠀⇛ Haunted Chocolatier is the next game from Stardew Valley creator ConcernedApe (Eric Barone), we still don’t yet know a huge amount about it but the dev recently showed some fresh screenshots. These are just some small teasers, with Barone mentioning on their Twitter to expect plenty more throughout 2022. On December 25, Barone mentioned the game is “making good progress” and currently work is progressing on the “core elements of the game”. We don’t expect to get a lot of info before a true full reveal, as Barone mentioned “I don’t really feel like sharing much, because I’d rather let the game be a surprise than reveal everything. I just like working in secret”. # ⚓ Tiny_Life_is_an_upcoming_pixel-art_take_on_experiences_like The_Sims_|_GamingOnLinux⠀⇛ Tiny Life is an upcoming game trying to capture the essence of games like The Sims, but in an isometric pixelart style. If you’ve played The Sims before, you mostly know sort-of what to expect from it. Build a house, have a family and take care of all their needs – or totally mess with them. You’re basically god watching over a few select people. Tiny Life’s creator, the solo indie developer Ellpeck, has always loved casual life simulation games like The Sims, Harvest Moon and Stardew Valley. For multiple years, he deemed the prospect of making a complex life simulation game similar to The Sims too difficult, until he started working on Tiny Life and realized that it is, indeed, quite the task. Nevertheless, he has been working on the game regularly for over a year and considers it his passion project. # ⚓ Linux_Play:_Baldur’s_Gate:_Dark_Alliance,_Shadow_Tactics: Aiko’s_Choice,_The_Captain_…_–_itsfoss.net⠀⇛ We close 2021 and in 2022 with the latest edition of Linux Play, our premiere games section for Linux with the best of what came out in December, or much of it. And nice things came out: Baldur’s Gate: Dark Alliance, new installment of the veteran and award-winning RPG franchise; Shadow Tactics: Aiko’s Choice, another new installment, in this case the most recent, but also applauded real-time strategy franchise set in ancient feudal Japan; The Captain, which is new from the creators of World of goo… And so on until reaching the ten titles that make up the list, topped as always by an eleventh game, this free one: the musical Tempo. Linux Play! # ⚓ The_Best_Linux_Games_of_2021_–_itsfoss.net⠀⇛ We are already in 2022 and not only that: today we celebrate the Day of the Magi, a very beloved holiday here in Spain because that is when the gifts arrive, although for some time now, he has been in fierce conflict with Santa Claus. Be that as it may, this holiday allows us to publish a special like the one at hand, in which we collect the best games of the year for Linux, screening through, yes. This special Linux Play we select a list with The 10 best games that came out for Linux in 2021, which should be clarified, because what is said to play on Linux can be done in many ways and with quite a few guarantees: you can play the most outstanding releases through platforms of streaming like Stadia or GeForce Now, you can play more and more titles with better quality through Steam and Proton … However, in this Linux Play: The Best Games of 2021 only native games are includedNot because there are great differences between playing one or the other, beyond the details of each platform, but, as we have always done, for consistency, but also for “necessity”: native games are the most significant indicator of the health of Linux gaming… Although in the last couple of years the appearance of the aforementioned Proton has destabilized everything. # ⚓ ChimeraOS_29_brings_fixes_for_Aya_Neo,_GPD_Win_3_and_more upgrades_|_GamingOnLinux⠀⇛ Continuing to refine the SteamOS-like full-screen experience, ChimeraOS 29 is out now bringing on upgrades and plenty of bug fixes too. The usual main components have been upgraded including Linux Kernel 5.15.12, Mesa drivers 21.3.3, NVIDIA driver 495.46, RetroArch 1.9.14 and upgrades to their own special helper packages too. Users of a few handhelds will be happy too with ChimeraOS 29 bringing fixed WiFI on the Aya Neo 2021 Pro/Retro Power, there’s now a touch-screen driver for the GPD Win 3 and another hardware fix is to stop the ASRock LED controller being recognized as a joystick. # ⚓ The_Steam_Deck_is_the_biggest_gaming_news_of_all_time._– Invidious⠀⇛ # ⚓ Liftoff:_FPV_Drone_Racing_gets_a_huge_physics_update,_new racing_environment_|_GamingOnLinux⠀⇛ Liftoff: FPV Drone Racing is a very good simulator and it just got that little bit better, with update 1.4.0 out now bringing some major improvements. Going back to the drawing board for the physics system, LuGus Studios decided to rely less on Unity’s built-in physics with their new flight controller, the result is that overall in many places it should perform better. Something that also sounds fancy is a new ” A.I. PID tune feature” that will adjust “itself based on the system’s performance for a perfectly tuned setup in light” but you can still tune things manually. # ⚓ Canonical_wants_to_position_Ubuntu_as_the_benchmark_for Linux_Gaming⠀⇛ Canonical has posted a job offer with which you intend to hire a Desktop Video Game Product Manager (newly created role) “to make Ubuntu the best Linux desktop to play“. Undoubtedly a declaration of intent by the company, which is possibly aware that 2022 may be a turning point for the company. Linux Gaming. Canonical gets chest out when explaining in the offer that it works “With partners in the silicon world to ensure the latest graphics drivers and settings are incorporated to achieve optimal latency and frame rates, as well as partners in the video game industry to ensure mechanisms such as anti-aging capabilities. -traps are available to ensure equity and product availability “. Nothing to object here, because if you want to attract talent, obviously the company has to sell. Regarding the functions and / or responsibilities that the possible future employee would exercise, it is worth highlighting that of leading the product and the launch of video games to the market oriented to the Ubuntu desktop. Being more specific, this person would be in charge of define product strategy and commitments around Ubuntu desktop and will try to drive adoption. We doubt that this leads to any kind of exclusivity, but rather to make the Canonical distribution the reference operating system of the Linux Gaming. The company founded by Mark Shuttleworth explains that “The position requires an analytical storyteller with a strong sense of message and a deep understanding of Linux communities and desktop, video game and graphics technologies”. In terms of curriculum and characteristics, college graduates with experience in software engineering and software engineering management with aspirations to be executives and entrepreneurs are preferred. # ⚓ Ubuntu_Seeks_a_Gaming_Product_Manager_to_Build_Cred_With Gamers_–_FOSS_Force⠀⇛ Ubuntu might be on its way to becoming a Linux distribution that’s more suitable for Linux gamers by default. Canonical, the company behind Ubuntu, has posted a job listing on it’s website for a “Linux desktop gaming product manager.” Since its first release in 2004, Ubuntu has been one of the most used desktop Linux distributions (the most used if you factor in all of the “official” Ubuntu spins — Ubuntu clones integrating desktop environments other than Ubuntu’s default Gnome). The distro gets quite a bit of use by Linux gamers too, but not as much as you might think given its popularity. The fact is, its popularity among everyday desktop users probably accounts for much of the use it gets from gamers, since Linux users enter the gaming realm on whatever distro they’ve been using, then move own to something that can better deliver the oomph that gaming requires. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Wireless_network_does_not_auto-reconnect_in_KDE⠀⇛ This is a fairly short tutorial, but the problem is quite annoying. It’s a small thing, but it does mar the overall experience. Thinking more broadly, the credentials management in Linux is a bit weird, and hasn’t been properly done since, well, ever. Some desktop environments will prompt you to use password wallets, some won’t. Some distros will or won’t, regardless of the desktop you use. There will be situations where you launch a particular app, like Chromium or Skype, and the wallet tool will wake up. Sometimes, network share connections will need password again and again, because the system won’t use the wallet. All of this goes beyond MX Linux and the re- connect issue I’ve outlined above. But if you are affected, take a look at the Wireless settings, see if all users can connect, and optionally, activate KDE Wallet so that you have a bit more elegant and secure setup in place. Problem solved. And that would be all for this time, folks. # ⚓ Krita_5.0.2⠀⇛ Hot on the heels of Krita 5.0.0, we’re releasing the first bugfix release of Krita 5! It’s 5.0.2 because if you upload a beta with the version number 5.0.0 to the Windows Store, you cannot upload 5.0.0 final, but it has to be 5.0.1… So, don’t worry, you didn’t miss 5.0.1! o § Distributions⠀➾ # ⚓ Solus_Again_Navigating_Rough_Seas_as_Co-lead_Quits⠀⇛ There’s been something of a brouhaha at the Linux distribution Solus OS, a popular independent distro that’s available with its own homegrown Budgie desktop environment, Gnome, Mate, or KDE. The result is that Joshua Strobl, a co-lead at the project, has abruptly stepped down. News of the situation became available on New Year’s Day when Strobl sent the following tweet… # ⚓ Haiku_activity_report_–_December_2021⠀⇛ Happy new year! Note: this report covers changes only to the Haiku main git repository. There are many other things going on for Haiku outside that git repository. In recent big news, we have an X11 compatibility layer, and a running experimental Wine port. However, I cannot cover everything in these reports. Help welcome if you want to contribute to our website with news announcements for such items. That being said, let’s see what’s going on in Haiku itself! This report covers hrev55688-hrev55768. # § SUSE/OpenSUSE⠀➾ # ⚓ openSUSE-Based_GeckoLinux_Kicks_Off_2022_with_New Major_Releases_of_Its_Editions⠀⇛ It’s been more than seven months since the last GeckoLinux update, and now it’s time for a new one that brings cool new features, the latest desktop environments, and many other improvements. The GeckoLinux ROLLING edition is probably the most popular, so it now ships with the KDE Plasma 5.23.4, GNOME 41.2, Xfce 4.16, LXQt 1.0, Cinnamon 5.2.4, MATE 1.26, Budgie 10.5.3, as well as the Pantheon desktop environment from elementary OS 6.1. # ⚓ GeckoLinux_ROLLING_Released_with_Updated_Desktop Environments⠀⇛ The latest GeckoLinux ROLLING release brings Linux kernel 5.15 and a set of updated desktop environments to its users. GeckoLinux is a Linux distribution based on openSUSE. It is available in two editions: Static, which is based on openSUSE Leap, and Rolling, which is based on openSUSE Tumbleweed. Compared to openSUSE, GeckoLinux provides some extra packages, including multimedia support, and live ISOs files for eight different desktop environments: Cinnamon, Xfce, GNOME, KDE Plasma, MATE, LXQt, Budgie, and Pantheon. For people who want something lighter, Gecko offers a nine Barebones edition. # § Slackware Family⠀➾ # ⚓ LibreOffice_7.2.5_packages_for_Slackware-current⠀⇛ LibreOffice Community Edition 7.2.5 was released yesterday and I have uploaded a new set packages for Slackware-current. This is the fifth iteration in the 7.2 release cycle with two more to come in the next three months. Since this is a minor upgrade, the focus is on bug fixing and improving the stability. # § IBM/Red Hat/Fedora⠀➾ # ⚓ Why_you_should_migrate_your_Java_workloads_to OpenShift⠀⇛ Despite the incredible pace of adoption of container orchestration platforms such as Kubernetes and Red Hat OpenShift, the vast majority of Java workloads are still running on virtual machines or bare metal. In many cases, enterprise operation teams are mandated to modernize and move these workloads to the cloud, and OpenShift is the natural destination. # ⚓ Red_Hat’s_2022_Global_Tech_Outlook_report_reveals active_participation_in_the_Financial_Services_and Banking_sectors⠀⇛ Red Hat’s yearly survey, the 2022 Global Tech Outlook report, consolidated industry input and responses to questions related to digital transformation efforts across industry categories. In this article, we’ll look at some key takeaways in the report from the Financial Services and Banking sector. Among the areas cited to help attain an effective digital transformation strategy in Financial Services and Banking included closing talent gaps, accelerating application development, and establishing a hybrid cloud platform. # ⚓ Debug_.NET_applications_running_on_Kubernetes_with_VS Code [Ed: IBM's Red Hat is once again boosting Microsoft's proprietary lock-in]⠀⇛ # ⚓ IBM_wrongly_sacked_salesman_after_Tech_Data_project failed_•_The_Register⠀⇛ An IBM salesman was wrongly sacked after being blamed for the failure of a joint venture with Tech Data, being subject to a “biased, superficial and wholly inadequate” redundancy scoring exercise by vindictive sales managers. Craig Millard won his claim against IBM for unfair dismissal in December 2021, having been turfed out of Big Blue 18 months ago when a two-year secondment to Tech Data ended. The tribunal’s resulting judgment revealed how a combination of high prices, bad management, and a “ground breaking” joint venture that collapsed after achieving just 21 per cent of its sales targets resulted in IBM bosses breaking the law when they got rid of him. Luke Jones, IBM’s UK Technology Support Services (TSS) sales leader, was responsible for awarding Millard poor performance scores (41 out of 100) that led to him getting the professional axe in late 2020. # ⚓ IBM_Cloud_suffers_global_provisioning_issues_•_The Register⠀⇛ IBM is having a torrid start to 2022, including a lengthy period of “provisioning issues” in IBM Cloud around the world this morning. Today’s upset kicked off at 0546 UTC, according to the company’s status page, and continued throughout the morning, with Big Blue not flagging the problem as resolved until 1212 UTC. According to Big Blue: “Users may experience issues with provisioning and other resource management actions in IBM Cloud services.” Somebody snarkier than us might take issue with the use of the plural “users” considering the company’s lowly share of the cloud market. Not us, though. According to IBM Cloud, the locations affected were Washington DC, Osaka, São Paulo, London, Dallas, Seoul, Sydney, Chennai, Toronto, Tokyo, and Frankfurt. # § Canonical/Ubuntu Family⠀➾ # ⚓ Linux_Mint_20.3_“Una”_Xfce_released!⠀⇛ The team is proud to announce the release of Linux Mint 20.3 “Una” Xfce Edition. Linux Mint 20.3 is a long term support release which will be supported until 2025. It comes with updated software and brings refinements and many new features to make your desktop even more comfortable to use. # ⚓ Linux_Mint_20.3_“Una”_MATE_released!⠀⇛ This new version of Linux Mint contains many improvements. For an overview of the new features please visit… # ⚓ Linux_Mint_20.3_“Una”_Cinnamon_released!⠀⇛ The release notes provide important information about known issues, as well as explanations, workarounds and solutions. To read the release notes, please visit… # ⚓ You_Can_Now_Upgrade_Linux_Mint_20.2_to_Linux_Mint 20.3,_Here’s_How⠀⇛ Still based on the Ubuntu 20.04 LTS (Focal Fossa) operating system series, Linux Mint 20.3 “Una” is now available and it brings a new app to manage your recent and favorite documents, improvements to many of the official Linux Mint apps, as well as updated packages. Linux Mint 20.3 uses the same package base as Linux Mint 20.2, and all previous updates in the Linux Mint 20 series for that matter. This means that you can easily upgrade your existing installations without downloading the new ISO images, which are here mostly for new deployments. # ⚓ The_Future_of_Snapcraft⠀⇛ System hysteresis, when applied to software, can roughly be defined as an overall lag between desired implementation of code and actual implementation of said code. Ideally, this delay should be minimal, and programmers would be able to make instantaneous changes and improvements to their applications. In reality, things are more complex – and tend to get more complex as time goes by. For the past six odd years, the Snapcraft team has worked on making their core product modular, efficient and useful to snap developers, extending its functionality and introducing new capabilities over time. In a way, it is a complete product, and it serves its purpose well. But there are ways to make things even better. This article looks at the future of Snapcraft. # ⚓ Canonical_Outlines_the_‘Future_of_Snapcraft’⠀⇛ # ⚓ Canonical_To_Focus_On_A_New,_More_Modular_Snapcraft_– Current_Codebase_Goes_Legacy⠀⇛ # ⚓ Canonical_is_reworking_Snap_application_packages_on Linux⠀⇛ Snap is a software packaging and distribution platform for Linux developed by Canonical, creators of Ubuntu Linux. Snap applications are more portable than traditional Linux software, and most of them are containerized to prevent some common security issues. However, Snap also has plenty of problems, which might be the reason Canonical is experimenting with a new architecture. Canonical talked about “the future of Snapcraft” in a new blog post (via omg! ubuntu!), which mostly involves breaking up the Snap framework into smaller and modular components. There aren’t any firm details about what the end result will look like, or if it will be better for the average person installing and using Snap applications. However, it should make creating and maintaining Snap applications easier for app developers and Canonical, which could potentially free up time for Canonical to focus on other aspects of the Snap framework. # ⚓ Technology_can_sometimes_go_from_east_to_west:_Ubuntu DDE_21.10_remix_ships_in_22.01⠀⇛ The newest and quite possibly shiniest Ubuntu remix has kicked a new version out the door. Yes, yet another new desktop, but it’s a sign of bigger things to come. Ubuntu DDE stands for Ubuntu Deepin Desktop Edition – in other words, a remix of Ubuntu but with the desktop environment of the Chinese Deepin distro. Deepin, formerly known as the no-less-silly-sounding Hiweed, is the free international edition of a Chinese government-backed enterprise distro called UOS. Deepin is based on Debian, and switched desktops quite a few times in its early versions until UnionTech developed its own desktop environment. We don’t tend to hear much about it in the Western world, but open-source operating systems have been making great leaps forward in East Asia. At the turn of the century, the region was notorious for its use of pirated software. The problems with updates and malware this caused, plus a desire to reduce dependence on American companies that mirrors Western mistrust of Chinese vendors, led to Beijing’s “3-5-2 policy” to phase out foreign hardware and software. This is scheduled to happen by the end of 2022. One of several results is KylinOS, which started out based on FreeBSD but moved to Linux with its third version. Since 2013, there’s also been an Ubuntu-based variant. The Reg installed Deepin, Ubuntu Kylin and Ubuntu DDE for a quick look, and came away impressed. # ⚓ Dell_announce_the_new_XPS_13_Plus_with_Ubuntu supported_|_GamingOnLinux⠀⇛ During CES 2022 Dell announced the brand new XPS 13 Plus, which overhauls the design and it looks pretty slick. They’ve confirmed that Ubuntu 20.04 will also still be a supported option, on their Developer Edition. “Our most powerful XPS 13 was redesigned from the ground up to be our highest-performing flagship ever, so users can do everything they love faster. New modern and simplified interiors are beautiful and provide a seamless touch experience for customers. Stunning displays and enhanced audio bring your content to life. Crafted of machined aluminum and glass in Platinum or Graphite.” — Dell. o § Devices/Embedded⠀➾ # ⚓ New_batch_of_AstroPis_set_up_on_International_Space_Station •_The_Register⠀⇛ A new batch of AstroPi computers are up and running on board the International Space Station (ISS), set-up by ESA astronaut Matthias Maurer. The units were shown off in September 2021 and launched aboard a SpaceX Dragon 2 freighter atop a Falcon 9 rocket in December. They are to replace the existing AstroPi units “Ed” and “Izzy” which have resided on the ISS for six years. Maurer spent yesterday afternoon on the ISS setting up the new kit, which consists of Raspberry Pi 4 Model B hardware, a 12.3MP camera, and a range of sensors. Engineers will eventually be able to control the units from the ground and upload code submissions from the Mission Zero and Mission Space Lab programs. Both are aimed at getting young people interested in coding, with one teaching participants how to write a program to take a humidity reading and display a message (without swears) to the astronauts while the other is a more complicated team-based affair. # § Mobile Systems/Mobile Applications⠀➾ # ⚓ Google_Pixel_Android_12_bugs,_problems,_&_issues tracker⠀⇛ # ⚓ These_are_the_Android_brands_you_should_pay_attention to_in_2022_|_Android_Central⠀⇛ # ⚓ Sony_Android_TV_unresponsive_to_Google_Nest/Home Assistant_commands⠀⇛ # ⚓ Nebula_launches_Android_TV_app_for_creator-centric service_–_9to5Google⠀⇛ # ⚓ The_Best_Games_On_Sale_for_Android_This_Week_– Pavilion,_Arrog,_Jydge_and_More_–_Droid_Gamers⠀⇛ # ⚓ 5_best_auction_apps_for_Android_–_Android_Authority⠀⇛ # ⚓ Android_Circuit:_Galaxy_S22_Ultra_Specs_Leak,_Tales Of_Oppo_And_OnePlus,_Four_Nokias_For_America⠀⇛ # ⚓ How_to_set_up_emergency_SOS_features_on_Android⠀⇛ # ⚓ Android_12_is_now_rolling_out_to_unlocked_Samsung Galaxy_Note20_units_in_the_US⠀⇛ # ⚓ Nokia’s_latest_C-_and_G-series_phones_will_launch with_Android_12_out_of_the_box_–_NotebookCheck.net News⠀⇛ # ⚓ Sony_Xperia_1_III_and_Xperia_5_III_start_receiving stable_Android_12_update⠀⇛ # ⚓ Sony_Android_12_update_tracker:_List_of_eligible devices,_release_date_&_…⠀⇛ # ⚓ How_to_Block_Unknown_Numbers_on_Android⠀⇛ # ⚓ OnePlus_9_review:_The_end_of_an_era⠀⇛ # ⚓ Android_phones_with_physical_keyboards_aren’t_dead yet⠀⇛ # ⚓ MEmu_Android_Emulator_7.6.5_–_Neowin⠀⇛ # ⚓ What_Is_Hidden_Cache_In_Android?_–_Fossbytes⠀⇛ # ⚓ Android_TV’s_popularity_skyrockets_as_it_passes_110 million_monthly_active_devices⠀⇛ # ⚓ Unlocking_Android_Phones_With_Wear_OS_Watches_Is Finally_Happening⠀⇛ # ⚓ Meta_abandons_its_own_Oculus_Quest_OS_in_favor_of Android._For_now,_at_least_|_Android_Central⠀⇛ # ⚓ Android_Vs_iOS:_Which_Is_More_Secure?⠀⇛ # ⚓ Google_announces_updates_for_cars_compatible_with Android_Auto_and_Google_built-in_–_Times_of_India⠀⇛ o § Free, Libre, and Open Source Software⠀➾ # § Web Browsers⠀➾ # ⚓ Brave_vs._Google_Chrome:_Which_is_the_better_browser for_you?⠀⇛ Google Chrome is undoubtedly one of the best web browsers available for Linux. It offers a good blend of user experience and feature set for many, regardless of what platform you use it on. On the other hand, Brave is popular as a privacy-focused open-source option available cross-platform. So, what should you pick as your primary web browser? Is Chrome for you? Who should use Brave? Here, we compare all the important aspects (including benchmarks) on both browsers to help you decide. # ⚓ The_Optional_Chaining_Operator,_“Modern”_Browsers, and_My_Mom⠀⇛ I wanted to try and explain to my Mom that, while true for many native applications, browsers shouldn’t go out of date so easily because of hardware. “This isn’t your problem Mom. You should’t have to go buy new hardware. This is a problem with the people who make that website. They should be making their website’s code more accessible to legacy devices. Just because you don’t have a browser that can run ECMAScript 2020, you should still be able to access and use this website.” But I didn’t feel like explaining the idea of progressive enhancement to my Mom. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ LibreOffice:_The_Klingons_and_Interslavs_are_already here⠀⇛ While Klingon language support still ranks somewhat low among issues thought not to be essential, the federation that is LibreOffice 7.3 will also bring Interslavic support to the mix when released come early February. Since you were wondering, Interslavic is an artificial language meant to operate in the cross-section of Slavic interlingualism. Targ-herders everywhere are reportedly mildly pleased. The synergy in KSL (Klingon as second language) regions is a potato harvest that we can all appreciate. # § Programming/Development⠀➾ # § Perl/Raku⠀➾ # ⚓ My_Favorite_Warnings:_closure⠀⇛ In the context of Perl, a closure is a piece of code that captures a specific instance of a lexical variable. A blog entry a month or so ago explores this in greater detail. If you review this blog entry, though, note that it does not cover lexical subroutines, which act more like anonymous subroutines even though they are named. # ⚓ Perl_Weekly_Challenge_146:_Prime_Numbers_and Fraction_Tree⠀⇛ o § Standards/Consortia⠀➾ # ⚓ The_web0_manifesto⠀⇛ The web0 manifesto: a short and sweet middle finger to web3. * § Leftovers⠀➾ o ⚓ Stay⠀⇛ o ⚓ LEGOpunk_Orrery_Knows_Just_The_Right_Technics_|_Hackaday⠀⇛ Is the unmistakable sound of the shuffling of LEGO pieces being dug through burned into your psyche? Did the catalog of ever more complex Technic pieces send your imagination soaring into the stratosphere and beyond? Judging by the artful contraption in the video below the break, we are fairly certain that [Marian] can relate to these things. No doubt inspired by classic orreries driven by clockwork, [Marian]’s LEGO Sun-Earth-Moon orrery is instead driven by either hand cranks or by electric motors. The orrery aims to be astronomically correct. To that end, a full revolution of a hand crank produces a full day’s worth of movement. o § Science⠀➾ # ⚓ Another_test_for_divisibility_by_7⠀⇛ Recently I thought of another way to check for divisibility by !!7!!. Let’s consider !!\color {darkblue}{3269}!!. The rule is: take the current total (initially 0), triple it, and add the next digit to the right. So here we do: [...] o § Education⠀➾ # ⚓ Chicago_Teachers_Rebuke_‘Incompetent’_Mayor_Lightfoot_as Lockout_Continues_for_Second_Day⠀⇛ Classes across Chicago Public Schools were canceled for the second consecutive day Thursday as city officials refused to allow teachers to work remotely despite rising coronavirus cases and what the Chicago Teachers Union says are inadequate safety precautions in school facilities. The union filed an unfair labor practices charge with the state labor relations board late Wednesday, saying Democratic Mayor Lori Lightfoot and school officials failed to put proper public health measures in place before students and staff returned to school on Monday following the holiday break. # ⚓ Leaving_academia⠀⇛ I’ve previously spent about two years time intermittently working in industry settings. I enjoyed the fast pace and working on problems that have a human on the other side waiting for your solution. o § Health/Nutrition/Agriculture⠀➾ # ⚓ The_Dairy_Industry_is_Determined_to_Pour_Itself_Down_Our Throats⠀⇛ The real American dream is at odds with turning taxpayer dollars into wealth for one industry over another. An example of this is the promotion of the American dairy industry by the government. It’s the reason why the United States Department of Agriculture (USDA) has been telling people that dairy deserves its own food group and has promoted the idea that most adults and children should “eat or drink about three cups of dairy each day,” to ensure they are getting the required nutrients to stay healthy. This is, however, contradictory to the facts provided by the National Institutes of Health. According to the agency, between 30 and 50 million Americans are intolerant to lactose (the sugar found in milk), “including 95 percent of Asian Americans, 60-80 percent of African Americans and Ashkenazi Jews, 80-100 percent of Native Americans, and 50-80 percent of Hispanics,” compared to people of northern European descent who have a “high lactose tolerance.” In fact, some studies connect the consumption of dairy products with a higher risk of certain cancers, including prostate cancer in men and endometrial cancer in postmenopausal women. Further, countries that have the highest rates of milk consumption also have the “highest rates of osteoporosis.” According to a study by Uppsala University in Sweden, the consumption of milk has even been associated with higher mortality in both men and women, according to a 2014 article in the Washington Post. # ⚓ We’re_All_Tired_of_This_Pandemic—and_Some_of_Us_Are_Sick⠀⇛ # ⚓ Omicron_Outbreaks_in_Prisons_Put_Everyone_at_Risk,_But_Data Is_Scarce⠀⇛ # ⚓ What_Will_We_Tell_Future_Generations_About_the_Pandemic?⠀⇛ # ⚓ Opinion_|_Vaxxed_or_Unvaxxed:_Who_Should_Get_the_Last_Bed Hospital_Bed?⠀⇛ Novak Djokovic, the world’s top-ranking tennis player, has just been granted a medical exemption to take part in the Australian Open. Djokovic, who has won the event nine times (one more victory would give him a record-breaking 21 major titles), refused to show proof of vaccination, which is required to enter Australia. “I will not reveal my status whether I have been vaccinated or not,” he told Blic, a Serbian daily, calling it “a private matter and an inappropriate inquiry.” # ⚓ I_Saw_Firsthand_What_It_Takes_to_Keep_COVID_Out_of_Hong Kong._It_Felt_Like_a_Different_Planet.⠀⇛ As I walked off the jet bridge into Hong Kong International Airport, I stepped into another world. I was home for Christmas, to see my parents for the first time in two years. But first, I had to get through a gantlet of COVID-19 precautions that envelop the city like a protective bubble. Incoming travelers were greeted by gowned, gloved and masked workers, who directed us through the terminal. As I followed the passengers ahead of me, I was unnerved by the shuttered stores. Every other time I’ve flown in and out of Hong Kong, the airport hums with thousands of travelers, children scampering across the polished floors, announcements intoned in English, Cantonese and Mandarin. The terminal was now eerily still. My feet made too much noise as I trudged along the path marked by guardrails. # ⚓ CIA_Introduces_Sustainable_Food_Systems_Master’s_Degree⠀⇛ The Culinary Institute of America, the world’s premier culinary college, announced a new addition to its School of Graduate and Professional Studies: an online master’s degree in Sustainable Food Systems. Now enrolling for Fall 2022, this program is the first of its kind to approach sustainability issues—from climate change to renewable resources, waste reduction to responsible sourcing and more—through a culinary lens, with an eye toward the impact of our choices on our food system, both today and in the future. This is the CIA’s third master’s program, joining its master’s degrees in Food Business and Wine and Beverage Management. The predominantly online 30-credit curriculum offers candidates the flexibility of learning on their own schedule, while continuing to advance in their careers, and includes short, immersive in-person residencies in the San Francisco Bay Area and New York’s Hudson Valley, which provide opportunities for real-world experiential learning and industry networking. # ⚓ Canadian_‘influencers’_stranded_in_Cancún_after_party flight_from_Montreal⠀⇛ In the videos, the influencers can be seen drinking, smoking, dancing and even crowd-surfing, all without face masks, in their December 30 charter flight. The videos were originally posted by the plane party’s participants, then later deleted. In the posts, the party-goers could be seen passing bottles of alcohol and dancing in the aisles. In response, the charter company, Sunwing, canceled the group’s return flight. Other Canadian airlines have followed suit, refusing to accommodate the group on a return flight. o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # ⚓ Google_Chrome_97_relaxes_privacy_protection_just_a little_to_help_out_Microsoft [Ed: Microsoft is_an espionage_giant]⠀⇛ Google Chrome 97 arrived on Tuesday, bringing with it a Microsoft-backed keyboard API rejected by Apple and Mozilla on privacy grounds. # ⚓ Remember_Norton_360′s_bundled_cryptominer?_Irritated folk_realise_Ethereum_crafter_is_tricky_to_delete⠀⇛ Norton antivirus’s inbuilt cryptominer has re-entered the public consciousness after a random Twitter bod expressed annoyance at how difficult it is to uninstall. The addition of Ncrypt.exe, Norton 360′s signed cryptocurrency-mining binary, to installations of Norton antivirus isn’t new – but it seems to have taken the non-techie world a few months to realise what’s going on. Back in June, NortonLifeLock, owner of the unloved PC antivirus product, declared it was offering Ethereum mining as part of its antivirus suite. NortonLifeLock’s pitch, as we reported, was that people dabbling in cryptocurrency mining probably weren’t paying attention to security – so what better way than to take up a cryptocurrency miner than installing one from a trusted consumer security brand? # ⚓ Norton’s_Antivirus_Product_Now_Includes_an_Ethereum Miner⠀⇛ Norton 360 can now mine Ethereum. It’s opt- in, and the company keeps 15%. # ⚓ Norton_360_Now_Comes_With_a_Cryptominer⠀⇛ Norton 360, one of the most popular antivirus products on the market today, has installed a cryptocurrency mining program on its customers’ computers. Norton’s parent firm says the cloud-based service that activates the program and allows customers to profit from the scheme — in which the company keeps 15 percent of any currencies mined — is “opt- in,” meaning users have to agree to enable it. But many Norton users complain the mining program is difficult to remove, and reactions from longtime customers have ranged from unease and disbelief to, “Dude, where’s my crypto?” # ⚓ US_online_pharmacy_Ravkoo_links_data_breach_to_AWS portal_incident⠀⇛ # § Security⠀➾ # ⚓ Alibaba_Cloud_slapped_by_Chinese_ministry_for mishandling_Log4j [Ed: Western authorities have done worse things to people who reported and tried to fix bugs, e.g. "WalwareTech"]⠀⇛ China’s Ministry of Industry and Information Technology has suspended Alibaba Cloud’s membership of an influential security board to protest its handling of the Log4j flaw. The move appears odd as The Apache Software Foundation credited Alibaba Cloud’s Chen Zhaojun for identifying and reporting the Log4J flaw in the first place. You might think Alibaba Cloud deserves a parade for identifying a dangerous flaw, and showing that Chinese bug-hunters can match it with the world’s best. But according to Chinese outlet The 21st Century Herald, Chinese authorities were displeased with the cloud giant’s response. # ⚓ Security_updates_for_Friday_[LWN.net]⠀⇛ Security updates have been issued by Debian (sphinxsearch), Fedora (chromium and vim), Red Hat (rh-nodejs14-nodejs and rh-nodejs14-nodejs-nodemon), and Ubuntu (apache2 and webkit2gtk). # § Privacy/Surveillance⠀➾ # ⚓ The_VPN_Is_On_Everybody’s_Shitlist_After Years_Of_Scammy_Providers_And_Empty Promises⠀⇛ The high number of scammy providers and overall rise in encryption appears to have turned the public sentiment against virtual private network (VPN) VPNs, and whether most consumers actually even need one. As privacy scandals and hacks grew over the last decade, VPNs quickly emerged as a sort of mystical panacea, that could protect you from all harm on the internet. Of course, this resulted in a flood of VPN competitors who were outright scams, made misleading statements about what data is collected, or failed to protect consumer data. # ⚓ France_fines_Google,_Facebook_record_€210 million_over_tracking_online_activity⠀⇛ US tech giants, including the likes of Apple and Amazon, have come under growing pressure over their [business] practices across Europe, where they have faced massive fines and plans to impose far-reaching EU rules on how they operate. The 150-million-euro fine imposed on Google was a record by France’s National Commission for Information Technology and Freedom (CNIL), beating a previous cookie-related fine of 100 million euros against the company in December 2020. Facebook was handed a 60-million- euro fine. # ⚓ “Worst_in_Show_Awards”_Livestreams Friday:_EFF’s_Cindy_Cohn_and_Cory_Doctorow Will_Unveil_Most_Privacy-Defective,_Least Secure_Consumer_Tech_Products_at_CES⠀⇛ # ⚓ How_are_Police_Using_Drones?⠀⇛ But how are police departments using them? A new law in Minnesota mandates the yearly release of information related to police use of drones, and gives us a partial window into how law enforcement use them on a daily basis. The 2021 report released by the Minnesota Bureau of Criminal Apprehension documents use of drones in the state during the year 2020. According to the report, 93 law enforcement agencies from across the state deployed drones 1,171 times in 2020—with an accumulative price tag of almost $1 million. The report shows that the vast majority of the drone deployments are not used for the public safety disasters that so many departments use to justify drone use. Rather, almost half (506) were just for the purpose of “training officers.” Other uses included information collection based on reasonable suspicion of unspecified crimes (185), requests from other government agencies unrelated to law enforcement (41), road crash investigation (39), and preparation for and monitoring of public events (6 and 12, respectively). There were zero deployments to counter the risk of terrorism.  Police deployed drones 352 times in the aftermath of an “emergency” and 27 times for “disaster” response. # ⚓ France_fines_Meta,_Google:_Cookies_must be_easier_to_reject_•_The_Register⠀⇛ Google and Facebook have come a little unstuck in the cookie department as French watchdog Commission Nationale de l’Informatique et des Libertés (CNIL) slapped the pair with a €150m and €60m fine respectively. The CNIL kicked off its investigations after receiving complaints regarding the way cookies can be refused on facebook.com, youtube.com and google.fr. The crux of the matter is that while there is a button to permit immediate acceptance of cookies, there is not the equivalent to refuse them as easily. “Several clicks are required to refuse all cookies, against a single one to accept them,” explained the CNIL. “The restricted committee,” it went on, “considered that this process affects the freedom of consent: since, on the internet, the user expects to be able to quickly consult a website, the fact that they cannot refuse the cookies as easily as they can accept them influences their choice in favor of consent. This constitutes an infringement of Article 82 of the French Data Protection Act.” o § Defence/Aggression⠀➾ # ⚓ ‘Don’t_Abandon_Us’:_Palestinian_Rights_Group_Rebukes_Dutch Government_for_Halting_Funding⠀⇛ Human rights advocates condemned the Dutch government’s Wednesday decision to stop funding the Union of Agricultural Work Committees, one of six Palestinian civil society groups that Israel designated as “terrorist organizations” and banned almost three months ago. “The Union of Agricultural Work Committees (UAWC) is shocked and saddened by the decision of the Dutch government to end its funding for UAWC,” the group, based in Ramallah, a city in the occupied West Bank, said in a statement. “With this fateful decision, the Dutch government is not just abandoning UAWC, but Palestinian civil society at large.” # ⚓ Noam_Chomsky:_GOP’s_Soft_Coup_Is_Still_Underway_One_Year After_Capitol_Assault⠀⇛ # ⚓ Opinion_|_Did_Horror_of_January_6_Crush_Your_Optimism?_Try “Possibilism”_Instead⠀⇛ A new year is supposed to trigger the energy of new beginnings, requiring at least a bit of optimism. Right? But at the anniversary of January 6th—a day of national infamy—optimism and it companion, hope, can feel out of reach. # ⚓ A_Year_Later,_Progressives_Warn_‘Another_January_6′_Is Coming_If_Voting_Rights_Not_Secured⠀⇛ One year to the day since then-President Donald Trump and his Republican accomplices’ lies about voter fraud led to a failed coup on January 6, 2021, progressives are warning that the GOP’s ongoing, nationwide assault on the franchise will continue as long as Senate Democrats fail to pass pro-democracy legislation. “365 days after the attacks on the 2020 election culminated in the Capitol calamity, we still haven’t enacted meaningful reforms to prevent another January 6.” # ⚓ In_the_UK,_Calls_Grow_to_Revoke_Tony_Blair’s_Knighthood Over_Iraq_War⠀⇛ Citing his role in the Iraq War and other devastating conflicts, hundreds of thousands of people in the United Kingdom and beyond are calling for former British Prime Minister Tony Blair to be stripped of his newly bestowed knighthood.  “He was personally responsible for causing the death of countless innocent civilian lives and servicemen in various conflicts.” # ⚓ The_War_on_Terror_is_a_Success…for_Terror⠀⇛ Days earlier, Congress had authorized Bush “to use all necessary and appropriate force against those nations, organizations, or persons he determine[d] planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001 or harbored such organizations or persons.” By then, it was already evident, as Bush said in his address, that al-Qaeda was responsible for the attacks. But it was equally clear that he had no intention of conducting a limited campaign. “Our war on terror begins with al-Qaeda, but it does not end there,” he announced. “It will not end until every terrorist group of global reach has been found, stopped, and defeated.” Congress had already assented to whatever the president saw fit to do. It had voted 420 to 1 in the House and 98 to 0 in the Senate to grant an Authorization for Use of Military Force (AUMF) that would give him (and presidents to come) essentially a free hand to make war around the world. # ⚓ The_Anti-War_Movement_Could_Be_Reignited_By_Gen_Z⠀⇛ Every system of oppression upholds every other system of oppression, and the oppression of war — whether in its traditional form of bases and boots on the ground or through more modern methods such as drone strikes and economic sanctions — is no exception. Gen Z has an essential role to play in uniting existing progressive movements like the climate movement and Black Lives Matter. At the same time, we need to foster a strong anti- imperialist angle in every single struggle against injustice. Gen Z can — and must — bring new life to anti-war activism. Our future depends on it. # ⚓ The_American_torch_of_democracy_is_flickering⠀⇛ For Americans, the stakes are high. American identity, unlike that of most nations, is rooted not in blood or ethnicity but in self-evident truths of human equality. Through the embrace of such ideals, immigrants to the United States become, as Abraham Lincoln put it, the “blood of the blood and the flesh of the flesh” of all other Americans. Those ideals make the American nation. The political expression of that national identity, rooted in universal truths, is democracy. Give that up and the United States is no longer a “new nation, conceived in liberty.” We would degenerate into an ethno-state, a white man’s country along the lines of the Confederacy—and, if former President Donald Trump and his circle have their way, a tyranny. The stakes for the world are high as well. American democracy has inspired the world’s democratic movements for longer than many think. After the Union’s victory in the Civil War, the French abolitionist and liberal Édouard René de Laboulaye wanted to celebrate what he and others saw as a twin victory of liberty over the slave state that was the Confederacy and of democracy over chaos or tyranny. He conceived of a great Statue of Liberty to mark that victory. She still stands in New York Harbor, her torch held aloft as inspiration for Europe and the world. # ⚓ Jimmy_Carter:_I_Fear_for_Our_Democracy⠀⇛ Lastly, the spread of disinformation, especially on social media, must be addressed. We must reform these platforms and get in the habit of seeking out accurate information. Corporate America and religious communities should encourage respect for democratic norms, participation in elections and efforts to counter disinformation. Our great nation now teeters on the brink of a widening abyss. Without immediate action, we are at genuine risk of civil conflict and losing our precious democracy. Americans must set aside differences and work together before it is too late. # ⚓ US_Army_journal’s_top_paper_from_2021_says_Taiwan_should destroy_TSMC_if_China_invades⠀⇛ A top US Army War College paper suggests Taiwan should credibly threaten to eradicate its semiconductor industry if threatened by China so that Beijing would no longer be interested in unification. The US Army War College showed the paper was its most popular of the year, when it revealed it topped a list of the most downloaded papers of 2021 from its quarterly academic journal Parameters. The bright idea comes from two American scholars. Their reasoning goes: Potential war with the US over Taiwan is no longer a deterrent for China as Beijing believes its military would dominate. Therefore, to make the island unappealing, it needs to be perceived as presenting an “unacceptable economic, political, and strategic costs upon Beijing.” As it currently stands, Taiwan appears to be an enticing technology powerhouse ripe for absorption. However, destroying TSMC, an important supplier for China, would create a desperately unwanted major economic crisis on the mainland and make China chipless while it was also engaged in a war effort. o § Transparency/Investigative Reporting⠀➾ # ⚓ Pentagon_Drone_Attacks_Killed_Many_Innocent_People_with Impunity⠀⇛ This argument that the exposure of war crimes cost lives is absurd. It was not Assange that carried out drone attacks and other bombing operations against innocent civilians and journalists. The lives were taken by the Pentagon based upon imperialist designs to control large swaths of territory in Central, South and West Asia along with Africa. It was the Pentagon war planes directed by high-ranking military officials, intelligence operatives and politicians that killed and maimed millions over the last two-to-three decades. In addition to the mass killings, tens of millions more have been internally displaced and turned into refugees. The political, economic and military institutions of the U.S. and NATO countries are the ones that require prosecution, imprisonment and dismantlement in order for corrective justice to be achieved. o § Environment⠀➾ # ⚓ Defusing_the_Global_Climate_Emergency_Depends_on_Defusing the_Democracy_Emergency⠀⇛ This story originally appeared in The Guardian and is part of Covering Climate Now, a global journalism collaboration strengthening coverage of the climate story. # ⚓ Opinion_|_Defusing_Democracy_Emergency_Needed_to_Address Climate_Emergency⠀⇛ A year ago today, Mitch McConnell and Kevin McCarthy were fleeing for their lives as a violent mob swarmed the halls of the US Capitol. With their personal safety at risk, the two most powerful Republicans on Capitol Hill at last stood up to Donald Trump. In a heated phone call, McCarthy, the House minority leader, fruitlessly implored the president to call off the mob. Senate majority leader McConnell later called the rioters “terrorists” and said Trump was “morally responsible” for the violence. # ⚓ Protecting_US_Democracy_and_Climate_Action_Are ‘Inseparable,’_Green_Groups_Tell_Congress⠀⇛ As people across the United States this week look back on last year’s January 6 insurrection, environmental advocacy groups came together to remind federal lawmakers and President Joe Biden that efforts to protect U.S. democracy and tackle the climate emergency are fundamentally connected. “Democracy, climate action, human rights, social equity, and environmental justice are inseparable.” # ⚓ Echoing_Climate_Deniers,_Washington_Post_Op-ed_Imagines Electric_Cars_Stuck_in_Snow_Instead_of_Gas_Ones⠀⇛ Originally published by ClimateDenierRoundup on Daily Kos. No one wants to get stuck in traffic. Or in the snow. Getting stuck in an all-day traffic jam because it snowed, well, that’s pretty much the worst. And that’s exactly what happened in Virginia this week, when hundreds of drivers spent all day stuck on the highway after a severe snowstorm turned a jackknifed semi from a relatively routine highway occurrence to a major SNAFU. # ⚓ Carbon_Justice_and_Global_Survival⠀⇛ If one would combine emissions from Australia’s exports with its local emissions, Australia contributes a colossal 3% to 4% to the world’s entire emissions. With a population less than the city of Shanghai (26.4 million), Australia (25.69 million) remains the world’s 6th largest emitter behind super-polluters like the USA, China, India, Russia and Japan. Globally, 76% of all emission are from fossil fuels to which corporations operating in Australia make a sizable contribution. Some of these corporations are what the philosopher Jeremy Moss calls carbon majors: BHP, Glencore, Yancoal, Peadbody, AngloAmerican, Chevron, Whitehaven, Woodside, ExxonMobil, and Santos. Combining their emissions results in them being the world’s 8th biggest contributors to global warming. # ⚓ What_is_Pay-as-You-Throw?⠀⇛ Many cities and towns around the world, including over 7,000 in the U.S., have pay-as-you-throw waste policies. Examples include Seattle, Berkeley, Austin and Portland, Maine. Large cities often require residents to purchase special trash bags or stickers so that they pay separately for every bag of trash. Or people may have to sign up for a certain level of waste collection service, which limits how much garbage they can set out on the curb. # § Energy⠀➾ # ⚓ Prosecutor_Sought_Funding_From_Oil_Giant_Enbridge_to Jail_Line_3_Water_Protectors:_Report⠀⇛ With Canadian oil giant Enbridge pouring more than $4 million into a fund that was used by the law enforcement agencies which have arrested hundreds of people for protesting the company’s thousand-mile-long tar sands pipeline, the prosecutor who is bringing charges against the environmental defenders believed he was also entitled to benefit from the fund, according to an independent investigation. The Center for Protest Law and Litigation (CPLL) revealed Thursday that Jonathan Frieden, the lead prosecutor seeking to jail hundreds of opponents to the Line 3 pipeline, sought more than $12,000 last July from the so-called Line 3 Public Safety Escrow Trust, which the Minnesota Public Utilities Commission (PUC) ordered Enbridge to pay into as a condition of the pipeline’s construction. # ⚓ In_Disgusting_Waste,_Airlines_Are_Flying_Thousands_Of Completely_Empty_Jetliners:_The_Situation_Is_As Terrible_As_It_Is_Avoidable.⠀⇛ Want more proof that we’re living in a late- stage capitalism hellscape? Look no further than Europe, where tens of thousands of empty planes are being flown due to an air traffic rule — while needlessly polluting the skies. As the English-language Belgian magazine The Bulletin reports, the Germany-based airline Lufthansa has operated 18,000 empty flights this winter alone due to a European Union rule requiring airlines to operate at least half of their scheduled flights in order to keep their spots at airports. # ⚓ Lithium_batteries’_big_unanswered_question⠀⇛ As the world looks to electrify vehicles and store renewable power, one giant challenge looms: what will happen to all the old lithium batteries? # § Wildlife/Nature⠀➾ # ⚓ Globe_at_Night_2022:_Can_You_See_the_Stars?⠀⇛ Every year, the Globe at Night international community science campaign raises awareness about the impact of light pollution by inviting community scientists to measure and submit night sky brightness observations. All you need is a computer, tablet, or smartphone! And their webapp is now available in 28 languages! o § Finance⠀➾ # ⚓ Workers_at_First_Unionized_Starbucks_Walk_Off_Job_to Protest_Working_Conditions⠀⇛ # ⚓ We_Must_Have_Accountability_for_Corporate_Crime⠀⇛ Climate change has gone from the theoretical to slapping us in the face. From drought and fires that killed hundreds in California, to massive tornadoes ripping apart Kentucky, to sea-level rise and flooding cities, America is being hammered and Americans are dying.  Right now. # ⚓ Opinion_|_Child_Tax_Credit_Ends,_But_Corporate_Giveaways Continue⠀⇛ Last week I suggested that Trump maintains a hold on a large fraction of America because he fills a void created by a system that has left them behind. I followed with the question raised by Frank Capra’s iconic film “It’s a Wonderful Life,” in which the greedy Mr. Potter tries to take over Bedford Falls: Do we join together or let the Potters of America own and run everything? # ⚓ Opinion_|_Corporations_Are_Selling_Out_Democracy_for Political_Influence⠀⇛ One year ago, the foundation of our democracy was jeopardized in a full-blown coup attempt by seditionists egged on by former president Donald Trump. People died. # ⚓ Green_Party_calls_for_an_end_to_gross_CEO_pay_inequality_on Fat_Cat_Friday⠀⇛ The Greens are calling for CEO salaries to be no more than 10 times the amount that their company’s lowest-paid workers receive, arguing that the Covid-19 pandemic has shown more than ever the harmful impacts of inequality. # ⚓ Counterpoint_on_Venture_Capital⠀⇛ My personal experience working with VCs was very positive, but it was (a) a long time ago and (b) they were top-flight firms (Sutter Hill and Sequoia). I’ve been very skeptical of the current state of the VC industry in Venture Capital Isn’t Working and Venture Capital Isn’t Working: Addendum. Steven J. Dubner’s Is Venture Capital the Secret Sauce of the American Economy? presents a far more optimistic view, as does The Economist’s The bright new age of venture capital. On my side of the argument are Fred Wilson’s Seed Rounds At $100mm Post Money and the Wall St. Journal’s The $900 Billion Cash Pile Inflating Startup Valuations. Below the fold, some discussion of these opposing views. o § AstroTurf/Lobbying/Politics⠀➾ # ⚓ Randall_Kennedy_Says_It_Loud⠀⇛ For over three decades, Randall Kennedy, the Michael R. Klein Professor at Harvard Law School, has made one bold intervention after another in the most pressing social issues of the day. Not only has he written at length on such subjects as interracial marriage, affirmative action, and crime and policing, but his work has touched off controversies regarding his nuanced defense of the “politics of Black respectability,” his thinking on racial nomenclature and the variety of ways for describing the collective identity of Black Americans, and his critiques of “anti-racism gone awry” on college campuses. # ⚓ Treasonous_Clowns⠀⇛ # ⚓ A_Recall_Referendum_in_Venezuela_will_be_a_Failure_If Attempted⠀⇛ Author Roger Harris offers a 2021 political review of our Latin-American and Caribbean region vis-a- vis the United States and he notes accurately the “popular electoral victories in Chile, Honduras, and Peru”. Then we had the landslide re-election of president Daniel Ortega in Nicaragua and the major victory of Venezuela’s governing party PSUV in the regional and municipal elections that consolidated the support for the Bolivarian revolution even when “the extreme right opposition (including Guaidó’s party) was compelled to participate, implicitly recognizing the Maduro government.” But the extreme right opposition (at odds with the democratic opposition that participated in the elections and accepted the results) may already be plotting its next move in order to produce the regime change master minded by the US in Venezuela. The plot involves a referendum to recall president Nicolas Maduro. # ⚓ A_Warning:_Will_the_2024_Election_End_U.S._Democracy?⠀⇛ On the 6th, this force congealed around an autocratic leader, a complicit political establishment, a legion of enraged supporting troops and a hefty bankroll.  This force is redefining the political landscape.  Most consequential, they may win the 2024 presidential election and end U.S. democracy. The U.S. begins the new year as a nation besieged by an economic recession, overwhelmed by a global pandemic, witness to endless invocations of a new Cold War and powerless in the face of an ever- deepening environmental crisis.  No wonder for many the Trump insurgency seems but just another wave in an increasingly turbulent sea. # ⚓ Sir_Tony_Blair:_Bloody_Knight_of_the_Realm⠀⇛ The recently knighted Tony Blair is certainly not one to bother.  His name appeared in the Queen’s New Year’s Honours list, having been made a Knight of the Most Noble Order of the Garter.  “It is an immense honour,” came the statement from the foundation that bears his name, “to be appointed Knight Companion of the Most Noble Order of the Garter, and I am deeply grateful to Her Majesty the Queen.” Others begged to differ.  Within hours, a petition launched by Angus Scott calling for the rescission of the award garnered thousands of signatures.  (To date, the number is 755,879.)  The award, says the petition, is “the oldest and most senior British Order of Chivalry.”  It asserts that Blair “caused irreparable damage to both the constitution of the United Kingdom and to the very fabric of the nation’s society.  He was personally responsible for causing the death of countless innocent, civilian lives and servicemen in various conflicts.  For this alone he should be held accountable for war crimes.” # ⚓ Opinion_|_Famous_Last_Words:_I_Was_There_When_Democracy Fell⠀⇛ During this just-behind-us holiday season, occasionally I cruised our zillions of television channels and watched some movies, and it occurred to me that once upon a time, and not too long ago, on almost every one of our TV shows and in our films, bullies and crooks were the enemy. # ⚓ “Why_Was_the_Federal_Gov’t_So_Unprepared?”_Newsweek Reporter_William_Arkin_on_Jan._6⠀⇛ One year since Trump supporters staged a violent mob attack on the U.S. Capitol in an attempt to stop the certification of Joe Biden’s presidency, we discuss exactly what was happening behind the scenes in the intelligence community that day. We are joined by Newsweek national security reporter William Arkin, who appeared on Democracy Now! just hours prior to the Capitol attack and predicted a violent outcome hours later. Arkin says the intelligence community failed to prepare for the strength of Trump’s movement and needs to beef up its approach in anticipation for the next insurrection or coup attempt. “It’s really stunning to me that we haven’t looked more closely at what the role of the federal agencies were, what the intelligence was and what the intelligence agencies knew,” says Arkin. # ⚓ Grisham_Says_Trump_“Gleefully”_Watched_as_Loyalists Attacked_Capitol_a_Year_Ago⠀⇛ # ⚓ Over_150_Pro-Democracy_Groups_Demand_Schumer_Urgently Change_Senate_Rules_to_Pass_Voting_Rights⠀⇛ On the anniversary of the January 6, 2021 right- wing attack on the U.S. Capitol, over 150 national and local pro-democracy organizations released a letter demanding Senate Majority Leader Chuck Schumer change the Senate rules in order to reform the filibuster and pass voting rights legislation. “We believe that changing the rules to bypass Republicans’ continued obstruction is the only way to pass meaningful democracy legislation, and we urge you not to wait any longer.” # ⚓ Opinion_|_When_a_Sick_Nation_Comes_Apart_at_the_Seams⠀⇛ Let me start 2022 by heading back—way, way back—for a moment. # ⚓ Opinion_|_The_Utterly_Shocking_Things_Trumpers_and_His_GOP Believe⠀⇛ With the Republican Party turning to Trumpism, and the Democratic Party returning to their progressive roots, will we have an honest debate this election year in our media? # ⚓ McConnell-Backed_Election_Reform_Gambit_Is_a_Trap, Advocates_Warn⠀⇛ # ⚓ ‘It’s_a_Trap’:_Advocates_Warn_Against_McConnell-Backed Election_Reform_Gambit⠀⇛ Since June, Senate Minority Leader Mitch McConnell and his Republican caucus have filibustered three separate Democratic voting rights bills, refusing to permit even a floor debate on the legislation as GOP-led states intensify their assault on the franchise. But with Senate Democrats gearing up for yet another attempt to strengthen federal voter protections, McConnell is signaling a willingness to cooperate with the majority party on a far more narrow reform effort—one that would entail tweaks to the obscure Electoral Count Act. # ⚓ Ilhan_Omar_Warns_‘Next_Coup_Not_Only_Possible;_It_Has Already_Begun’⠀⇛ Congresswoman Ilhan Omar on Thursday marked the one-year anniversary of the January 6 assault on the U.S. Capitol with a dire warning to her fellow lawmakers and the nation: The next right-wing coup attempt “is not only possible; it has already begun.” With state-level GOP lawmakers moving to suppress the vote nationwide and insurrection-complicit Republicans still in positions of power in the U.S. Congress, Omar said in a statement that “the coup attempt on January 6th was a warning for what’s to come if we don’t act.” # ⚓ Tutu_Obits_Underplay_His_Advocacy_for_Palestine⠀⇛ Obituaries in the corporate and establishment press for South African Archbishop Desmond Tutu rightly celebrated him not only as one of the key leaders of the struggle against apartheid in his own country, but as a global advocate against oppression, including being a fierce Christian voice against homophobia. # ⚓ Biden_Is_Finally_Confronting_Trump’s_Big_Lie_—_But_There’s Much_Left_to_Do⠀⇛ # ⚓ Reform_the_Insurrection_Act:_Former_Pentagon_Adviser_Says Trump_Almost_Used_It_to_Subvert_Election⠀⇛ Former Pentagon adviser Ryan Goodman says former President Trump could have used the Insurrection Act to hold onto power during the January 6, 2021, attack on the Capitol by his supporters. “There needs to be reform of the Insurrection Act,” says Goodman, who authored the report “Crisis of Command: The Pentagon, the President, and January 6” for Just Security, where he is co-editor. He also discusses how Republican leadership from Congress, as well as agency heads from the FBI and the Justice Department, waged a coordinated response around Trump’s claims of voter fraud in an attempt to increase Republican voter turnout in Georgia. “The Justice Department used a lot of its resources, including the FBI investigations, to basically affect the outcome of the Georgia runoffs,” says Goodman. “That’s an extraordinary politicized use of the Justice Department and the FBI to do anything like that, to try to use it to shape an outcome of the election.” # ⚓ MSNBC_Host_to_Navarro:_Peaceful_or_Not,_Trump_Plot_to Overturn_Election_“a_Coup”⠀⇛ # ⚓ Elie_Mystal:_AG_Garland_Must_Be_More_Aggressive,_Hold_Trump &_Allies_Accountable_for_Insurrection⠀⇛ On the first anniversary of the deadly insurrection of January 6, when right-wing and white supremacist supporters of Donald Trump attacked the Capitol in an attempt to overturn the 2020 election, we speak with Elie Mystal of The Nation about the Department of Justice investigation, led by U.S. Attorney General Merrick Garland, who pledged Wednesday to bring everyone involved to “justice.” Mystal says Garland should be more aggressive and also pursue Donald Trump. “I want actual evidence that this man is willing to take on the powerful, politically connected Republicans who did this to us, and so far I don’t see that evidence,” says Mystal. So far, 725 rioters have been arrested on smaller charges. # ⚓ “White_Rage”_Author_Carol_Anderson:_GOP_Attack_on_“Election Fraud”_Really_an_Attack_on_Black_Voters⠀⇛ Many events marking the first anniversary of the deadly January 6 insurrection at the U.S. Capitol are focusing on voting rights, as false claims about voter fraud have fueled Republican efforts to restrict voting access, especially for Black voters. Senate Majority Leader Chuck Schumer vowed Tuesday to proceed with a vote to change the filibuster rule to prevent Republicans from blocking new voting rights legislation. Professor Carol Anderson, author of “White Rage” and “One Person, No Vote,” says former President Trump’s false claims about voter fraud prompted a wave in 2021 of some of the most aggressive and racist assaults on voting rights in recent U.S. history. “It is Jim Crow 2.0,” Anderson says of Republican voter suppression waged through state legislation. “It is designed to make sure we have minority rule in the United States, that we don’t have a democracy.” # ⚓ GOP_Attack_on_“Election_Fraud”_Is_Really_an_Attack_on_Black Voters⠀⇛ # ⚓ On_Anniversary_of_Insurrection,_Advocates_Demand_DC Statehood⠀⇛ As people nationwide marked the first anniversary of the U.S. Capitol attack amid rising concerns about American democracy, District of Columbia residents and advocates for full representation renewed calls for congressional action on D.C. statehood. “The safety of our community and the sanctity of our democracy are on the line.” # ⚓ Trump_Thrashed_for_Lie-Laden_Response_to_Biden_Jan._6 Anniversary_Address⠀⇛ Former U.S. President Donald Trump was raked Thursday for doubling down on his “Big Lie” that the 2020 presidential election was “stolen” in a series of spurious statements responding to President Joe Biden’s address marking the one-year anniversary of the deadly January 6, 2021 attack on the U.S. Capitol. “Attempting to overturn the election results and stop our country’s sacred tradition of a peaceful transition of power is divisive. Demanding accountability is not.” # ⚓ Moscow_calls_unrest_in_Kazakhstan_an_‘externally_incited’ insurrection_by_‘trained_and_organized_armed_formations’⠀⇛ Russian officials view this week’s protests in Kazakhstan as an “externally incited” attempt to undermine the security and integrity of the state, diplomats in Moscow announced in a statement published on the Foreign Ministry’s website on Thursday. # ⚓ Technically_legal_How_Kazakhstan_won_peacekeepers_from_a Russian-led_military_alliance⠀⇛ On January 6, Russian paratroopers from the Collective Rapid Reaction Force (KSOR) of the Collective Security Treaty Organization (CSTO) began arriving in Kazakhstan. This marked the start of the first military operation by the combined forces of the six former Soviet states that make up the military alliance, which has existed now for nearly 20 years. The legality of today’s operation in Kazakhstan is questionable, insofar as the use of collective force in the absence of external aggression against a CSTO member state is not codified in the organization’s charter (though neither is it strictly prohibited). In the past, CSTO members have been reluctant to treat domestic turmoil as a collective security threat. In fact, CSTO states have refused multiple times to deploy combined rapid reaction forces due to the lack of external aggression in a member country experiencing a crisis. # ⚓ Kazakhstan’s_revolt_continues_Thousands_arrested,_dozens killed,_and_gunfire_in_Almaty_as_authorities_crackdown_on protesters⠀⇛ With Kazakhstan under a state of emergency due to mass protests, the Collective Security Treaty Organization deployed troops to the country on January 6 to help quell the unrest. Earlier, Kazakhstani President Kassym-Jomart Tokayev issued several emergency orders to his cabinet, calling for the formation of a special group to carry out investigations and prosecutions regarding the demonstrations and rioting. Meanwhile, lines formed outside grocery stores, ATMs, and gas stations as people scrambled to buy food and fuel and withdraw cash. Banks have shut down across the country and Internet access remains intermittent. Tasked with dispersing the remaining demonstrators, the Kazakhstani Interior Ministry has vowed to “destroy” anyone who refuses to “lay down arms.” # ⚓ ‘This_is_a_turning_point’_In_a_dispatch_from_Almaty,_a local_journalist_shares_an_eyewitness_account_of_Kazakhstan’s uprising⠀⇛ Developments in Kazakhstan have evolved rapidly since demonstrations began on January 2. Under pressure from nationwide protests, President Kassym-Jomart Tokayev dismissed the cabinet and removed Nursultan Nazarbayev from his lifetime post as chairman of the National Security Council on January 5. By that evening, it appeared as though protesters had taken complete control of Kazakhstan’s largest city, Almaty. But the military soon returned to the city and launched an “anti- terrorist operation.” According to official reports, by the morning of January 6, dozens of protesters had died and police had arrested around 2,000 people. In a dispatch for Meduza, local journalist Aysulu Toyshibekova offers an eyewitness account from the streets of Almaty. # ⚓ From_‘demonstrators’_to_‘terrorists’:_How_Kazakhstani officials_changed_the_way_they_talk_about_the_unrest_now sweeping_the_nation⠀⇛ Protests in western Kazakhstan against suddenly doubled fuel costs began on January 2 and quickly spiraled into wider, nationwide unrest, including violent clashes with the authorities. Dozens have reportedly been killed in clashes, and police officials say several officers have died, as well. In cities like Zhanaozen, demonstrators’ demands have become more and more political. Following these developments, the nation’s authorities have also changed the way they talk about the unrest, using increasingly extreme rhetoric. # ⚓ Overnight_developments_in_Kazakhstan’s_uprising_CSTO peacekeepers_have_been_deployed,_and_an_‘antiterrorist operation’_is_underway_against_protesters_and_rioters⠀⇛ The Collective Security Treaty Organization has deployed troops to Kazakhstan, the organization confirmed officially to the news agency Interfax. The contingent of peacekeepers includes units from Russia, Belarus, Armenia, Tajikistan, and Kyrgyzstan. The decision to send soldiers was reached based on “the threat to the Republic of Kazakhstan’s national security and sovereignty caused, among other things, by outside interference,” Armenian Prime Minister and acting CSTO Collective Security Council Chairman Nikol Pashinyan explained in an announcement on Wednesday. # ⚓ US_war_lobby_fuels_conflict_in_Russia,_Ukraine,_and_Syria: ex-Pentagon_advisor⠀⇛ # ⚓ More_Russian_Cyber_Operations_against_Ukraine⠀⇛ # ⚓ [Old] UN_chief:_Dag_Hammarskjöld_‘set_the_highest_standard for_public_service’⠀⇛ Mr. Hammarskjöld was appointed Secretary-General in 1953, at just 47, still the youngest person to ever hold the UN’s top job. On 18 September 1961, during his second term, he died on a plane crash while en route to negotiate a ceasefire in the Congo. # ⚓ [Old] Dag_Hammarskjöld’s_Legacy_Endures_60_Years_on_from Ndola⠀⇛ On 18 September 1961, Dag Hammarskjöld and the persons accompanying him died tragically in a plane crash in Ndola, Zambia. Although his life was abruptly cut short, his legacy and ideals live on as a source of inspiration, as evidenced by the events held in his honour this month. # ⚓ [Old] Was_the_mysterious_death_of_Dag_Hammarskjold murder?⠀⇛ The third explanation is that another plane flew near the Albertina as it tried to land, either deliberately or accidentally, causing it to crash, either by forcing it to take evasive action or by downing it with warning shots. This would explain the eyewitness accounts, as well as tidbits other theories struggle with. In 2015 the UN reopened its investigation. Its first report found this explanation “plausible” and suggested that the governments involved ought to prove that they had made exhaustive checks of their records. It will report again in 2022. # ⚓ Opposition_activist_found_dead,_Omicron_gains_ground, Viktor_Orban_to_meet_Vladimir_Putin_and_a_plea_for_money⠀⇛ Gergely Homonnay , a Hungarian writer and political activist close to opposition party DK, was found dead in Rome. Homonnay has been living in Rome for a while. He published three books, each of which presented the events of the world from the perspective of his cat, Erzsi. o § Censorship/Free Speech⠀➾ # ⚓ Right-Wing_Hate_Speech_Runs_Rampant_in_India’s_Elections⠀⇛ The reference to “their” and “them” in her speech was clear to everyone in the room and anyone who watched her clip, which circulated widely on social media and on television channels in India. Sadhvi Annapurna was referring to the 204 million Muslims of India. “Even if 100 of us are ready to kill 20 lakh [2 million] of them, then we will be victorious and are ready to go to jail,” she said. Despite calls by some sections of society, including a group of retired government officials, to investigate and arrest the organizers and speakers of the Dharma Sansad for making these provocative hate speeches, the police in the state of Uttarakhand did not take any “serious action” against those who tried to incite violence through this event, stated government officials in a letter they sent to Uttarakhand’s Chief Minister Pushkar Singh Dhami “condemning his government’s response” to the Dharma Sansad. Uttarakhand is governed by the Bharatiya Janata Party (BJP), whose leader Narendra Modi is the prime minister of India. # ⚓ Lucille_Ball_may_have_prevailed_over_censorship,_but_on Dick_Van_Dyke’s_show,_it_was_another_story⠀⇛ “If you don’t air it,” Carl told them, “I’m walking off the show.” The episode was broadcast in Canada and though there were no letters of protest, the network refused to run it in America. Carl followed through on his threat, and Dick decided he didn’t want to go forward without him. After three seasons, the series went off the air. o § Freedom of Information/Freedom of the Press⠀➾ # ⚓ NPR’s_losing_top_talent_—_everyone_has_a_theory_why⠀⇛ However, before we fully get into it, I do want to say I wasn’t able to speak to any of these hosts directly, and I’m sure, one day, when they’re wanting to share more, we’ll receive the real reasons behind their leaving. Much of this is informed theorizing and feelings, and I think we all know the decision to leave a job is typically highly personal, so let’s assume there’s a combination of things happening, including the X factor of pandemic burnout and restlessness. Now, for what I’m hearing. # ⚓ Two_journalists_shot_dead_by_gang_in_Haiti⠀⇛ Two journalists in Haiti were killed Thursday by a gang operating on the outskirts of the capital Port-au-Prince, according to the radio station that employed one of the victims. o § Civil Rights/Policing⠀➾ # ⚓ The_Making_Of_A_Moral_Panic,_Courtesy_Of_The_NY_Times⠀⇛ We’ve been talking a bit lately about how the media creates moral panics, especially ones that blame social media for problems that are much more likely mostly created by the media themselves. # ⚓ Appeals_Court_Denies_Immunity_To_Bored_Cop_Who_Decided_To Turn_A_Natural_Death_Into_A_Murder⠀⇛ What happens when you add a bored cop to a cold case? Bad things. Very bad things. That’s the moral of the story conveyed by this Seventh Circuit Appeals Court decision [PDF]. # ⚓ Rethinking_Progress_in_a_Time_of_Crisis⠀⇛ The challenge is to continue to imagine and build alternatives to what Mary Berry has called “the siren song of limitlessness.” To this point, we’ve been woefully unable to resist that song, the result being tragic homogenization of the world under “extractive, reductive capitalism.” The loss of cultural diversity throughout the world is perhaps the single greatest tragedy of this process of homogenization. As Winona LaDuke has pointed out, “cultural diversity is as critical as biological diversity.” Indeed, genuine cultural diversity seems likely to be a precondition for responsible, future-oriented use of natural resources. The richness and diversity of human culture is the treasure to be protected because it is the source of the energy and ideas needed to reconsider prevailing thinking on the meaning of progress and growth. Cultural diversity is the “real, not token, human diversity,” allowing us to understand the world in different ways, ways that challenge the global system at the deepest levels of analysis. It is among the defining pathologies of our global civilization that it cannot imagine, much less comprehend, values that can’t be bought or sold in the capitalist market. To accept today’s idea of progress, one must take it for granted that the varying social and economic systems of all countries should be subsumed under a master global operating system, capitalism. As David C. Korten has noted, Proponents of capitalism like to call theirs a free market system. There is a benefit to refusing to grant them this, refusing to allow corporations and their servants in the state and the press to cloak themselves in the language of freedom and rugged individualism, as if capitalism isn’t a human- designed system of violence and theft. What will ultimately prove persuasive to those who have swallowed the dogmas of unlimited growth is they have misunderstood their cherished principle of free markets; they have used that principle, unobjectionable when properly understood, to defend a system that could hardly be more different from a legitimate free market. # ⚓ New_York_Times_Parent_Company_Interfered_With_Union Efforts,_Labor_Board_Says⠀⇛ # ⚓ Baltimore_Police_Union_Blames_City’s_Murder_Rate_On Defunding_Efforts_That_Never_Happened⠀⇛ In response to the killing of a Baltimore police officer, the head of the Baltimore police union, Mike Mancuso, has decided to accuse everyone who doesn’t love cops as being responsible for her killing. The statement from the Baltimore City Fraternal Order of Police (FOP) was delivered via Twitter, portraying itself as an “Open Letter to the People of Baltimore.” # ⚓ No_Other_Way_to_Live:_Why_Ai_Weiwei_Left_China⠀⇛ “I refuse to accept the idea that the state’s authority can’t be opposed, challenged, or interrogated. In the face of power, I would always be at a disadvantage, I knew, but I was a born contrarian, and there’s no other way for me to live except by taking an oppositional stance,” Ai Weiwei, China’s most famous artist and activist in exile, wrote in 1000 Years of Joys and Sorrows, an autobiography published in November. # ⚓ What_Conservative_Justices_Talk_About_When_They_Talk_About Religious_Liberty⠀⇛ We have reached the point where the US Supreme Court has become one of the greatest threats to public health and welfare in this country. At a moment when many thousands of people are falling ill every day with Covid and state legislatures are taunting the Supreme Court by passing hundreds of laws that blatantly violate long-recognized constitutional rights relating to gun safety, reproductive rights, and voting, the court’s conservative justices insist that the most pressing constitutional emergency today is a conjured threat to religious liberty. # ⚓ Homeland_Security_has_devolved_into_a_nearly_rogue_agency_— accused_of_spying_on_journalists_and_activists⠀⇛ # ⚓ Time_Is_All_We_Have._We_Can’t_Let_the_Boss_Take_It_From Us.⠀⇛ Unions fight for more pay for workers. But workers also need to have time for themselves and their friends and families. Overtime pay and raises can’t replace what we need more than anything else: our time back. # ⚓ Welcoming_Our_Robot_Overlords⠀⇛ Amazon has amassed a kind of empire that most colonizers, not to mention entrepreneurs, could only dream of. It has achieved massive scale at conventional standards: The company boasts a healthy market capitalization of nearly $1.7 trillion dollars, buoyed by a recent massive increase in profit margins as the pandemic forced many into online purchases. It’s responsible for 40 percent of all US e-commerce and nearly 10 percent of online retail sales on the entire planet. Its true source of imperial majesty, though, might not be the hundreds of millions of packages it ships per month at all, but something far more ephemeral: its “vast empire of customer data.” Maybe Amazon’s empire isn’t a group of executives that manage some important machines. Maybe Amazon’s empire is a machine. Our robot overlords are already here, and they came with articles of incorporation. o § Internet Policy/Net Neutrality⠀➾ # ⚓ Shitty_U.S._Broadband_Maps_Are_A_Feature,_Not_A_Bug⠀⇛ We’ve noted a few times now how the U.S. is preparing to spend $42 billion to shore up broadband access, despite not actually knowing where broadband is or isn’t available. It’s part of a multi-decade effort to fix mediocre broadband without using real world data to actually do it, and without acknowledging that the primary reason U.S. is mired in mediocrity is thanks to regional monopolization and the vast state and federal corruption that protects it. # ⚓ China:_Algorithm_law_for_„positive_energy“⠀⇛ The government in Beijing has passed a globally unique regulation for consumer protection on the internet # ⚓ Kazakhstan:_No_internet_and_cryptocurrency_problems⠀⇛ To stop protests, the government in Nur-Sultan restricts digital communication # ⚓ Massive_internet_outages_continue_to_sow_confusion_amid Kazakhstan_protests_–_The_Record_by_Recorded_Future⠀⇛ Nation-level internet traffic was cut off in Kazakhstan this week in the latest example of a petrostate trying to use shutdowns to quell protests and sow confusion. Early reports of communications disruptions started coming in on January 2, the first day people took to the streets in Almaty and other cities to protest fuel price increases and deteriorating economic conditions. Those reports were limited to localized mobile network interference and blocks on traffic to certain messaging services, including Telegram and Signal, Natalia Krapiva, Tech Legal Counsel at digital rights group Access Now said. The first wave of broad internet shutdowns started at 4:45 pm local time on January 5, according to data from network monitoring firm Kentik. Internet service was again disrupted early Thursday, according to NetBlocks. ⚠️ Confirmed: #Kazakhstan is again in the midst of a nation-scale internet blackout as of early morning Thursday. o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ To_End_‘Variant_Whack-a-Mole,’_Study_Says_World_Needs 22_Billion_More_mRNA_Vaccine_Doses⠀⇛ With the ultra-contagious Omicron strain pushing global Covid-19 cases to record highs, a new study published Wednesday estimates that the world needs 22 billion additional mRNA vaccine doses to overcome the surging variant and prevent future mutations from emerging. Compiled by public health experts at PrEP4All and Partners in Health in collaboration with scientists from Harvard Medical School and other prominent institutions, the study warns that current vaccine production capacity is nowhere near where it must be to ensure adequate inoculation rates in every country. # § Copyrights⠀➾ # ⚓ Parody_Post_About_Sega_Suing_Its_Fans_Perfectly Lampoons_Nintendo⠀⇛ We have long chronicled the aggressive IP enforcement tactics and behavior of video game giant Nintendo. There have been so many stories specifically about Nintendo’s animosity towards its fans when those fans express their fandom by creating fan-games that any regular reader here will be familiar with at least some of them. While gaming company responses towards fan-games are certainly more of a spectrum than something black and white, Nintendo probably takes the crown for the least permissive gaming company for this sort of thing. So much so, in fact, that we highlighted its former chief rival, Sega, when it took the opposite tact with folks making Sonic the Hedgehog fan-games. # ⚓ Top_Disney_Lawyer_To_Become_Top_Copyright_Office Lawyer,_Because_Who_Cares_About_The_Public_Interest?⠀⇛ People at the Copyright Office seem to get mad at me every time I suggest that the Copyright Office is captured by Hollywood, and pointing out how top officials there all seem to bounce back and forth between the Copyright Office and Hollywood. # ⚓ FBI_Arrests_Man_For_Fraudulently_Obtaining_Leaks_of 100s_of_Pre-Release_Books⠀⇛ The FBI has arrested a man who impersonated publishers and literary agents in order to fraudulently obtain hundreds of pre-release novels and other books in electronic form. Filippo Bernardini, 29, who worked at UK publisher Simon & Schuster, was detained upon arrival at JFK International Airport yesterday. # ⚓ Call_of_Duty_Cheat_Maker_‘EngineOwning’_Sued_By Activision_Under_The_DMCA⠀⇛ Activision has filed a copyright infringement lawsuit against business entities and individuals allegedly offering cheats for its Call of Duty games. According to the complaint, the defendants supply tools via EngineOwning.to that violate the anti- circumvention provisions of the DMCA, spoil the gaming experience for legitimate players, and damage Activision’s reputation. ䷩ 𝚕𝚒𝚗𝚎 6631 ╒═══════════════════ 𝐃𝐀𝐈𝐋𝐘 𝐋𝐈𝐍𝐊𝐒 ═════════════════════════════════════════════╕ ⠀⌧ █▇▆▅▄▃▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 01.07.22⠀▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▃▄▅▆▇█ ⌧ Gemini_version_available_♊︎ ✐ Links_8/1/2022:_Wine_7.0_RC5_and_Kdenlive_21.12.1⠀✐ Posted in News_Roundup at 8:08 pm by Dr. Roy Schestowitz 🄸🄼🄰🄶🄴 🄳🄴🅂🄲🅁🄸🄿🅃🄸🄾🄽 ⦇GNOME bluefish⦈ § Contents⠀➾ * GNU/Linux o Distributions o Devices/Embedded * Free_Software/Open_Source * Leftovers * § GNU/Linux⠀➾ o § Desktop/Laptop⠀➾ # ⚓ Librem_14_is_Ideal_for_Enterprise_Linux_–_Purism⠀⇛ While many people think of enterprise computers in terms of systems running Windows or MacOS, there have long been millions of enterprise users running a GNU/Linux-based enterprise Linux distribution and entire industries where all employees run Linux. While sometimes this is for philosophical reasons, often it’s also for practical reasons: a Linux desktop is the ideal development environment for instance, for writing software for the Linux servers that dominate the cloud. Picking hardware for the enterprise that runs Linux can be challenging for IT departments, but the Librem 14 is a drop-in replacement for any existing enterprise Linux laptop and makes deploying Linux in the enterprise easy. In this post we will outline some of the reasons why the Librem 14 is the ideal laptop for enterprise Linux. o § Audiocasts/Shows⠀➾ # ⚓ Vim_And_Emacs_Are_The_Most_Important_Skills_You_Should Learn_–_Invidious⠀⇛ I often get viewers asking me about what skills they should learn to become a “power user” or “elite.” While there are so many important skills that one could learn, I think the two most important programs that every Linux user owes it to themselves to learn are Vim and Emacs. o § Kernel Space⠀➾ # ⚓ Linux_5.17_GPU_Updates:_Raptor_Lake,_ADL-P_Stable, Raspberry_Pi_4K@60,_AMD_Seamless_Boot_–_Phoronix⠀⇛ While the Linux 5.17 merge window doesn’t open up until next week following Sunday’s Linux 5.16 stable debut, due to lead Direct Rendering Manager (DRM) subsystem maintainer David Airlie going on holiday next week he has sent out the feature pull early. Here is a look at the many GPU/display driver updates for this next kernel version. Some of the Linux 5.17 graphics/display driver highlights in the DRM subsystem include Alder Lake P graphics being declared stable (ADL-S was marked stable in Linux 5.16), initial Intel Raptor Lake S graphics support, continued DG2/Alchemist bring-up, support for laptop privacy screens within the DRM code, the Raspberry Pi VC4 DRM driver can now drive 4K @ 60Hz, AMD Seamless Boot for new hardware, and a variety of other improvements. o § Applications⠀➾ # ⚓ More_bug_reports_for_LiVES_video_editor⠀⇛ Just a couple of things to fix and intend to release EasyOS 3.2. One of those “things” is LiVES — I like it, very sophisticated, small because written in C++, gtk3-based, uses system libraries, doesn’t have rampant dependencies like some other video editors. However, it is buggy, for me anyway. o § Instructionals/Technical⠀➾ # ⚓ How_to_Upgrade_to_Linux_Mint_20.3:_The_Right_Way⠀⇛ In this article, I will walk you through the steps needed to upgrade to Linux Mint 20.3 from 20.2. As we informed you previously, the stable version of Linux Mint 20.3 “Uma” is officially out. If you are using Linux Mint 20.2, then you should already receive notification for upgrade. The upgrade process for all three Linux Mint editions i.e. Cinnamon, MATE, and Xfce is same. Before proceeding ahead, please ensure that the computer has a working internet connection. Here’s our Linux Mint 20.2 system before we start the migration process. # ⚓ Install_and_Configure_GitLab_on_Debian_11.⠀⇛ This time you will learn how to install and configure GitLab on Debian 11. GitLab is an open source code repository and collaborative software development platform for large DevOps and DevSecOps projects, written in Ruby and Go programming languages. It is quite a popular alternative to GitHub providing wiki, issue-tracking, and continuous integration and deployment pipeline features, using an open-source license, developed by GitLab Inc. # ⚓ Lock_your_camera_to_a_specific_USB_port_in_OBS_| Opensource.com⠀⇛ If you stream with OBS with multiple cameras on Linux, you might notice that cameras are loaded as they are detected during boot. You probably don’t give it much thought, normally, but if you have a permanent streaming setup with complex OBS templates, you need to know which camera in the physical world is going to show up in which screen in the virtual one. In other words, you don’t want to assign one device as Camera A today only to have it end up as Camera B tomorrow. To standardize a complex camera setup, you can impose some special rules on how cameras get assigned to locations in the Linux filesystem. # ⚓ Writing_Python_applications,_building_Linux_labs,_and_more tips_for_sysadmins_|_Enable_Sysadmin⠀⇛ Today, we are looking back at our top 10 articles of December to give you a chance to catch up on any of the great content you might have missed. In this list, you will see various topics covered, and we are confident that some, if not all, will be of interest to you. # ⚓ Vimtutor_–_make_VIM_lot_easier_to_Learn_for_newbies_–_TREND OCEANS⠀⇛ Enable Sysadmin wrapped up 2021 with a strong December. During the month, we published 24 new articles and received more than 691,000 reads from more than 470,000 readers across the site. For the full year, we achieved nearly 95% more page views compared to 2020, which we hope means that we’re providing more sysadmins the information they need to do their jobs well. # ⚓ Top_10_container_guides_for_sysadmins_|_Enable_Sysadmin⠀⇛ Each year, I get the opportunity to write a brief piece about the top container articles of the year that were published on Enable Sysadmin. It is a great opportunity to review and reread the articles. I am happy to see that a couple of mine made the cut. # ⚓ Three_Ways_To_Connect_Phone_And_Desktop!_~_The_Linux Ecosystem_~_–_Kockatoo_Tube⠀⇛ # ⚓ Wireless_network_does_not_auto-reconnect_in_KDE⠀⇛ Here’s an interesting, annoying little problem for you. Say you run a Linux machine, with the Plasma desktop as your UI of choice. You connect to a Wireless network, no sweat. But then, on reboot you discover that your system will not reconnect. The password is fine, and if you manually initiate the connection, everything works. Similarly, when you wake your machine (laptop) from sleep, there is no automatic reconnection to the access point. Manually, no problem. I discovered this issue in MX Linux MX-21 KDE recently. This is not something I’ve faced before, and I found this to be an unnecessary hurdle in an otherwise truly fine testing session. So I started looking through the system menus, and I soon found a rather simple, almost innocent and thus infuriating fix to this problem. Let’s see what gives. # ⚓ How_to_View_WebP_Images_on_Ubuntu_and_Linux_Mint⠀⇛ If you’ve searched for images on Google (or any other search engine), you’ve probably come across WebP images at some point but were perhaps hesitant to download them because of potential compatibility issues. Fortunately, though, there are workarounds to view WebP images on a computer. If you’re on Linux, you can do this in a few different ways. In this guide, we’ll explain WebP and walk you through the steps to view WebP images on Ubuntu and Linux Mint. # ⚓ How_to_Create_a_Kubernetes_Cluster_with_AWS_CLI⠀⇛ Elastic Kubernetes Service (EKS) is a managed Kubernetes service that is hosted on AWS. The main reason for using EKS is to remove the burden of managing pods, nodes, etc. Running Kubernetes in AWS currently requires a great deal of technical expertise and often falls outside the wheelhouse of many organizations. With EKS, the required infrastructure is managed by Amazon’s “in- house” team, leaving users with a fully managed Kubernetes engine that can be used either via an API or standard kubectl tooling. EKS will support all Kubernetes features, including namespaces, security settings, resource quotas & tolerations, deployment strategies, autoscalers and more. EKS will allow you to run your own control plane, but also integrates with AWS IAM so you can maintain your own access control to the API. # ⚓ How_to_install_Webull_Desktop_on_a_Chromebook_with Crossover⠀⇛ Today we are looking at how to install Webull Desktop on a Chromebook with Crossover 21. Please follow the video/audio guide as a tutorial where we explain the process step by step and use the commands below. # ⚓ Classic_SysAdmin:_How_to_Check_Disk_Space_on_Linux_from_the Command_Line_–_Linux_Foundation⠀⇛ Quick question: How much space do you have left on your drives? A little or a lot? Follow up question: Do you know how to find out? If you happen to use a GUI desktop (e.g., GNOME, KDE, Mate, Pantheon, etc.), the task is probably pretty simple. But what if you’re looking at a headless server, with no GUI? Do you need to install tools for the task? The answer is a resounding no. All the necessary bits are already in place to help you find out exactly how much space remains on your drives. In fact, you have two very easy-to-use options at the ready. o § Wine or Emulation⠀➾ # ⚓ WineHQ_–_Wine_Announcement_–_The_Wine_development_release 7.0-rc5_is_now_available.⠀⇛ The Wine development release 7.0-rc5 is now available. What's new in this release: - Bug fixes only, we are in code freeze. The source is available from the following locations: https://dl.winehq.org/wine/source/7.0/wine-7.0- rc5.tar.xz http://mirrors.ibiblio.org/wine/source/7.0/wine- 7.0-rc5.tar.xz Binary packages for various distributions will be available from: https://www.winehq.org/download You will find documentation on https:// www.winehq.org/documentation You can also get the current source directly from the git repository. Check https://www.winehq.org/git for details. Wine is available thanks to the work of many people. See the file AUTHORS in the distribution for the complete list. # ⚓ Wine_7.0-rc5_Released_With_Another_30_Bugs_Fixed_– Phoronix⠀⇛ Wine 7.0-rc5 is available for testing while the stable release of Wine 7.0.0 will be popped soon. The weekly release candidates of Wine 7.0 continue until being deemed in good enough shape for releasing v7.0.0 this month. In Wine 7.0-rc5 are another 30 bug fixes corrected this week. Among the fixes this week are for Roblox Player, Tropico 2, Logos Bible Software, Dying Light, Fallout 2, Cygwin, MSBuild, and a variety of other Windows games and applications. o § Desktop Environments/WMs⠀➾ # § K Desktop Environment/KDE SC/Qt⠀➾ # ⚓ Reunited_after_a_decade_–_Kai_Uwe’s_Blog⠀⇛ It’s been more than ten years since Dolphin, KDE’s versatile file manager, introduced its own custom QGraphicsView-based view engine. With that came more detailed view modes with grouping support, animated transitions, and a new places panel with sections. Unfortunately, it is all based on a now long- abandoned “Itemviews NG” project, and is inherently incompatible with Qt’s traditional model-view code used elsewhere in KDE. # ⚓ KDE_Plasma_will_put_the_turbo_to_finish_implementing Wayland⠀⇛ The project KDE has lived a very busy year 2021 due to the endless migration of Kwin to Wayland, the graphical protocol that has become the greatest eternal promise of the Linux desktop. But new years, new goals (or maybe not so much), so Nate Graham has posted on your blog a summary or part of the roadmap of KDE Plasma by 2022. To begin with, from the desktop environment they will continue polishing on those fronts where they still have to put things in order. For example, Nate Graham has recognized that language and format settings has so far been problematic because of overlap. Luckily, contributor Han Young is working to merge both sections and make appear on a single page. In this way, it would be clearer what is established in the system and, at the very least, it would make the possibility of incompatible configurations more difficult. Another point that will be renewed are the Breeze icons, Breeze in English. Designer Ken Vermette is working on modernizing and enhancing the Color Breeze icon theme to round out and soften them, as well as removing ugly and old elements like long shadows. On the other hand, the monochrome icons will also be renewed, all with the intention that both icon themes look better combined with the colors of the system and therefore polish the aesthetic finish. # ⚓ Maui_Report_17_–_MauiKit_—_#UIFramework⠀⇛ Today, we bring you a new report on the Maui Project’s progress. Maui 2.1 was released almost two months ago, and since then new features, bug fixes, and improvements have been made to the Maui set of apps and frameworks; the following blog post will cover some of the changes and highlights from the last month of development. # ⚓ Kdenlive_21.12.1_released_|_Kdenlive⠀⇛ The first maintenance release of the 21.12 series is out with fixes to ripple mode, project archiving and multiple bins. This version also enforces to transcode footage with variable framerates to a standard framerate value. # ⚓ Wallpaper_Livestream_(Part_2,_Sunday_January_9th)⠀⇛ For everyone who didn’t have a chance to attend, in the last livestream we started with the above sketch done in Krita and experimented with a new method on-the-fly where we leaned into Inkscapes snapping features to create a 3D mesh by hand, with the plan to use the built-in “Restacking” tool to enable hand-drawn polygons with “perfect” edges. While the mesh method was a rousing success and testing the restack feature gave ideal results, near the end of the stream it was realized that watching me draw triangles for several hours was not a hip idea, so I decided to take the remainder of the more tedious work offline. # § GNOME Desktop/GTK⠀➾ # ⚓ Felix_Häcker:_#25_The_Big_1.0⠀⇛ Update on what happened across the GNOME project in the week from December 31 to January 07. We wish everyone a Happy New Year! The new year starts right with a “Big 1.0”, Libadwaita – an important cornerstone for GNOME apps, had its first stable release! o § Distributions⠀➾ # § New Releases⠀➾ # ⚓ Makulu_Droid_new_Build_is_Live_!⠀⇛ Added GTK4 support. # § Screenshots/Screencasts⠀➾ # ⚓ Linux_Mint_20.3_“Una”_Cinnamon_overview_|_Sleek, modern,_innovative_–_Invidious⠀⇛ In this video, I am going to show an overview of Linux Mint 20.3 “Una” Cinnamon and some of the applications pre-installed. # § PCLinuxOS/Mageia/Mandriva/OpenMandriva Family⠀➾ # ⚓ KDE_Plasma_Application_Update_»_PCLinuxOS⠀⇛ The KDE Plasma Desktop application packages have been updated to 21.12.1. This is a service release update. # § SUSE/OpenSUSE⠀➾ # ⚓ openSUSE_Tumbleweed_–_Review_of_the_week_2022/01_– Dominique_a.k.a._DimStar_(Dim*)⠀⇛ First off, welcome to twenty-twenty-two, the year of the Linux desktop (wasn’t it?). The year is kicking off strong with openSUSE Tumbleweed – but not with daily snapshots: openQA did not agree with some of the changes (i.e one snapshot caused all non-x86_64 architectures to fail to boot, one snapshot had a broken virtualization stack, and of course, none of that made it to you, our users). Despite all that, we published 4 snapshots during this week: 20220101, 0102, 0103, and 0106. # § Slackware Family⠀➾ # ⚓ My_Docker_packages_for_Slackware-current⠀⇛ I have been using Docker for a while now, it’s being used to provide services to friends and family. I was always intimidated by the large amount of packages that were needed to get Docker and docker-compose up and running, and I did not have experience with Docker at the time (almost two years ago) so I decided to go the easy route and use the SlackBuilds.org scripts when I first needed to run a Docker container. I wrote a blog about that even, it explained how to run an Outline server to allow journalists to do their work in repressive countries but the article also shares the details how to build the Docker packages and run the daemon. If you want to read some background information about Docker’s strength and what its use-cases are, I encourage you to start reading here: https://docs.docker.com/get- started/overview/ . Essentially, Docker uses Linux kernel and filesystem capabilities to isolate an application and its dependencies from the host computer it is being executed on. Docker provides powerful means to connect multiple containers via internal (virtual) networking and can expose ports to the network outside of your container. It enables you to run applications reliably without having to worry about the underlying Operating system. You can even run Docker on a MS Windows computer but your containerized application running inside Docker will not be aware of that. This is sometimes called ‘light-weight virtualization’ because unlike real virtualization solutions like QEMU, Virtual Box or VMWare, the containerized application still runs on your host’s kernel. This is why you can run a 32-bit container image on a 64- bit (Linux 64-bit kernel has that capability to execute 32-bit binaries) host but you cannot run a 64-bit image on a 32-bit host kernel. # § IBM/Red Hat/Fedora⠀➾ # ⚓ IBM’s_original_‘Linux_man’_Irving_Wladawsky-Berger:_A New_Measurement_Framework_for_the_Digital_Economy⠀⇛ Several weeks ago I heard a very interesting keynote presentation by Cambridge professor Diane Coyle at the annual workshop of the Stanford Digital Economy Lab, – What Don’t We Know About Measuring the Digital Economy? Professor Coyle is also a research associate of the UK Economics Statistics Centre of Excellence. In 2017 she was a recipient of the Indigo Prize on how to measure economic activity in the digital economy for her essay Making the Future Count, co-authored with Benjamin Mitra-Kahn. “GDP captures only market transactions at the price of exchange, and not the welfare gains, externalities, environment, distribution of wealth or innovation which occurs in an economy,” wrote the authors. “Hence almost since its creation in the 1940s it has been criticised for its inability to capture economic welfare. Now changes in the economy, being restructured by digital technology and paying the price for unsustainable growth, make the case for a new measurement framework more pressing than ever. GDP was never an ideal measure of economic welfare and its suitability has been decreasing.” Gross Domestic Product (GDP) became the accepted international measure of economies in the1940s. While being a good measure for the 20th century industrial economy, GDP is a flawed measure for the 21st century economy. It was suitable when the economy was dominated by the production of physical goods, but GDP doesn’t adequately capture the growing share of services and other intangible assets that now characterize advanced economies. Nor does it reflect important economic activity beyond production, such as income, consumption and living standards. # ⚓ Remi_Collet:_PHP_version_8.0.15RC1_and_8.1.2RC1⠀⇛ Release Candidate versions are available in testing repository for Fedora and Enterprise Linux (RHEL / CentOS) to allow more people to test them. They are available as Software Collections, for a parallel installation, perfect solution for such tests, and also as base packages. RPM of PHP version 8.1.2RC1 are available as SCL in remi-test repository and as base packages in the remi-php81-test repository for Fedora 33-34 and Enterprise Linux. RPM of PHP version 8.0.15RC1 are available as SCL in remi-test repository and as base packages in the remi-test repository for Fedora 35 or in the remi-php80-test repository for Fedora 33-34 and Enterprise Linux. # ⚓ Fedora_Community_Blog:_Friday’s_Fedora_Facts:_2022- 01⠀⇛ Here’s your weekly Fedora report. Read what happened this week and what’s coming up. Your contributions are welcome (see the end of the post)! I have weekly office hours on Wednesdays in the morning and afternoon (US/Eastern time) in #fedora-meeting-1. Drop by if you have any questions or comments about the schedule, Changes, elections, or anything else. See the upcoming meetings for more information. # § Canonical/Ubuntu Family⠀➾ # ⚓ Linux_Mint_20.3_“Una”_released_[LWN.net]⠀⇛ Linux Mint has announced its 20.3 (“Una”) release for three different desktop environments: the Cinnamon, MATE, and Xfce editions. Mint 20.3 is a long-term support release, with support lasting until 2025. Each edition comes with a long list of new features (Cinnamon, MATE, and Xfce) and detailed release notes (Cinnamon, MATE, and Xfce). # ⚓ Ubuntu-on-a-phone_crowd_fix_Google_account_issues_in new_Touch_update⠀⇛ While some smartphone users are pondering when their next Android or iOS update will hit, the UBports foundation has released one for the Ubuntu Touch mobile operating system in the form of OTA-21. Still based on the Ubuntu 16.04 (although the team continues to work on 20.04) the update is due to hit supported devices (from the Google Pixel 3a to OnePlus hardware) during the coming week and has a number of useful tweaks. The most immediately visible is a change to what UBports call “the Greeter” (or the thing that appears when a user wants to unlock their device.) It’s all a bit slicker now, and has a different appearance depending on PIN or password selection. The storage statistics display has also received an overhaul and the Tamil language font added. o § Devices/Embedded⠀➾ # ⚓ Horizon_X3_AI_development_board_is_powered_by_Sunrise_3_AI Edge_Arm_processor_–_CNX_Software⠀⇛ After asking for some details, I was just told the SDK is based on Linux. # ⚓ CEEFAX_Lives!_(Courtesy_Of_A_Raspberry_Pi)_|_Hackaday⠀⇛ As analogue TV slides from memory, there’s a facet of it that’s fondly remembered by a band of enthusiasts. Teletext was an electronic viewdata information service digitally encoded in the frame blanking period, and a TV set with a decoder chip would provide access to many pages of news and other services all displayed in the characteristic brightly colored block graphics. It went the way of the dinosaur with the demise of analog TV, but for [Nathan Dane] the flame is kept alive with his own private version of the BBC’s CEEFAX service. # ⚓ Fanless_Alder_Lake-S_system_supports_extended temperatures⠀⇛ Vecow’s rugged “ECX-3000” runs Linux on a 12th Gen Alder Lake processor. The fanless embedded system has up to 8x 2.5G LAN with 4 PoE+, optional 2x 10GigE LAN, 4x front-access M.2 SSD trays, DC 9-50V and 40 to 75°C extended temperature support. # § Open Hardware/Modding⠀➾ # ⚓ Slither:_A_Visual_Pedometer_That_Sheds_Light_| Hackaday [Ed: Surveillance through "apps", which isn't good at all]⠀⇛ Have you already broken that New Year’s resolution to get more exercise? Yeah, us too. Maybe the problem is simply that we didn’t gamify the goal. A simple visual aid that shows your progress can help make a goal more achievable and easier to stick to, day after January day. That’s the idea behind [skhackett]’s Slither, the visual pedometer. [...] Although Slither uses the Fit Bit app, no actual Fit Bit is required — great news for those of us who don’t like to wear accessories. # ⚓ Tiny_LED_Matrix_Panels_Tile_Together_Perfectly_| Hackaday⠀⇛ There’s a lot to admire about LED matrix projects, which more often than not end up looking really cool. But most of them rely on RGB matrix panels sourced from the surplus market, and while there’s nothing wrong with that, building your own tiny, tileable LED matrix panels makes these builds just a little bit cooler. There’s a lot to admire about these matrix panels, not least of which is the seamless way they tile together. But to get to that point, [sjm4306] had a lot of prep work to do. He started with a much simpler 5×7 array, using the popular WS2812 RGB LEDs on a custom PCB. With a little practice under his belt, it was time to move to the much smaller SK6805 LEDs, which were laid out in an 8×8 matrix. The board layout is about as compact as it can be; [sjm4306] reports that it pushed the PCB fab to their limits, but he ended up with LEDs spaced perfectly on the board and just enough margin to keep consistent spacing in two dimensions when the boards are adjacent to each other. # ⚓ Board_with_25_RGB_LEDs_is_offered_with_ESP32-C3_or ESP32-Pico-D4_–_CNX_Software⠀⇛ In case you are in need of a tiny WiFI or Bluetooth-connected board with an RGB LED matrix, two have shown up on Banggood with basically the same 25 RGB LED design , except “C3FH4 RGB” board is based on ESP32-C3 RISC- V SoC, while the other, named “PICO D4 RGB“, features ESP32-Pico-D4 SiP (System-in- Package). # ⚓ PsyLink_An_Open_Source_Neural_Interface_For_Non- Invasive_EMG_|_Hackaday⠀⇛ We don’t see many EMG (electromyography) projects, despite how cool the applications can be. This may be because of technical difficulties with seeing the tiny muscular electrical signals amongst the noise, it could be the difficulty of interpreting any signal you do find. Regardless, [hut] has been striving forwards with a stream of prototypes, culminating in the aptly named ‘Prototype 8’ The current prototype uses a main power board hosting an Arduino Nano 33 BLE Sense, as well as a boost converter to pump up the AAA battery to provide 5 volts for the Arduino and a selection of connected EMG amplifier units. The EMG sensor is based around the INA128 instrumentation amplifier, in a pretty straightforward configuration. The EMG samples along with data from the IMU on the Nano 33 BLE Sense, are passed along to a connected PC via Bluetooth, running the PsyLink software stack. This is based on Python, using the BLE-GATT library for BT comms, PynPut handing the PC input devices (to emit keyboard and mouse events) and tensorflow for the machine learning side of things. The idea is to use machine learning from the EMG data to associate with a specific user interface event (such as a keypress) and with a little training, be able to play games on the PC with just hand/arm gestures. IMU data are used to augment this, but in this demo, that’s not totally clear. o § Free, Libre, and Open Source Software⠀➾ # ⚓ 30_startups_that_show_how_open_source_ate_the_world_in_2021 |_VentureBeat⠀⇛ It has been a busy year in the open source software sphere, from high-profile license changes to critical zero-day vulnerabilities that sent businesses into meltdown. But in among all the usual excitement that permeates the open source world, countless open source startups launched new products, attracted venture capitalist’s (VC) money, and generally reminded us of the role that open source plays in today’s technological landscape — including the data sovereignty and digital autonomy it promises companies of all sizes. Here, we take a look at some of the fledgling commercial open source companies that gained traction in the past year, revealing where enterprises and investors are betting on the power of community-driven software. # ⚓ Try_FreeDOS_in_2022_|_Opensource.com⠀⇛ Throughout the 1980s and into the 1990s, DOS was king of the desktop. Not satisfied with a proprietary version of DOS, programmers worldwide worked together to create an open source version of DOS called FreeDOS, which first became available in 1994. The FreeDOS Project continues to grow in 2021 and beyond. We’ve run several articles about FreeDOS on Opensource.com to help new users get started with FreeDOS and learn new programs. # § Web Browsers⠀➾ # § Mozilla⠀➾ # ⚓ After_heavy_criticism:_Mozilla_Foundation_no longer_accepts_donations_in_crypto_money⠀⇛ The Mozilla Foundation will no longer accept donations in cryptocurrency until further notice. Recently the foundation, which develops the free internet programs Firefox and Thunderbird, publicly reminded that donations are also accepted in crypto money. There was then strong criticism from many quarters that the generation of crypto currencies is climate-hostile and wastes energy. The Mozilla project explains on Twitter that the criticism has been received and the discussion about the impact of cryptocurrencies on the environment is being heard. Mozilla now wants to examine in detail whether crypto money is compatible with its own climate goals. This process is carried out transparently in the sense of open source. # ⚓ Firefox_skeleton_will_download_latest_Firefox⠀⇛ As we have ongoing issues with SeaMonkey, not working properly on some sites, we need to be able to easily install Firefox, Chromium or Chrome browsers. I very much like the SM suite, so want to keep it builtin to EasyOS. There are Firefox and Chromium SFS files, that can be downloaded via the “sfsget” icon on the desktop; however, I want a mechanism that is a single- click to install one of these browsers, and also a single-click (or a couple of clicks) to update to the latest version. So, I have created a PET ‘firefox-skel- ask’, that is just a skeleton, with various configuration files for Firefox. Most importantly, it has an entry in the menu “Internet -> Download latest Firefox”. First time you run this, it will download the latest version of Firefox, which right now is 95.0.2, and will set it up to run as user “firefox”. That is, it will run non-root, for enhanced security, and it’s home will be /home/ firefox # § SaaS/Back End/Databases⠀➾ # ⚓ Snowflake_named_DBMS_of_the_year_by_DB-Engines_•_The Register⠀⇛ It is joined in the top three by three-times previous winner PostgreSQL, which came second, and third-placed MongoDB, which took the top prize in 2014 and 2015. Rather than measuring database popularity on revenue — which would skew against FOSS systems — or basing its findings on downloads — which would include software downloaded for hobbyists, pilots, and tinkerers — DB-Engines bases its popularity score by amalgamating metrics. # § Productivity Software/LibreOffice/Calligra⠀➾ # ⚓ LibreOffice:_The_Klingons_and_Interslavs_are_already here_–_The_Document_Foundation_Blog⠀⇛ We happily report that Klingons have – at this point – not taken over control of the LibreOffice bug-tracker. While Klingon language support still ranks somewhat low among issues thought not to be essential, the federation that is LibreOffice 7.3 will also bring Interslavic support to the mix when released come early February. Since you were wondering, Interslavic is an artificial language meant to operate in the cross-section of Slavic interlingualism. Targ-herders everywhere are reportedly mildly pleased. The synergy in KSL (Klingon as second language) regions is a potato harvest that we can all appreciate. Undeterred by the confines of a monogalactic community of translators, LibreOffice numbers are growing. Hundreds of millions or earthlings alone now have powerful tools honed in their native languages. # § Programming/Development⠀➾ # § Perl/Raku⠀➾ # ⚓ Eertree:_Palindromic_Tree⠀⇛ The Task 2 of the Weekly Challenge #145 asked us to build a Palindromic Tree. It also linked to a blog post explaining the “Eertree” data structure. Maybe it was just me, but I found the blog post confusing. Fortunately, it further linked to a scientific paper that introduced the structure around 2014. I spent several evenings of the Christmas holidays wrapping my head around the description of the algorithm to efficiently build the graph. Most of it is described in the proof of Proposition 2, but some parts are rather laconic. I wasn’t able to implement the creation of a suffix link from P where |P| > 1. * § Leftovers⠀➾ o ⚓ Publishers_Clearing_House_Odds:_Not_Particularly_Good⠀⇛ America has quite a long history of lotteries and sweepstakes. Even George Washington participated as an investor in a lottery that included land, livestock and people (i.e. slaves) as prizes. The primary modern distinction between a lottery and a sweepstakes is that the latter cannot require purchase for entry. Otherwise, they effectively operate the same. States have a monopoly on lotteries. But sweepstakes can be very lucrative for private enterprise. Industry experts told the New York Times that the industry hit a stride in the 1960s as consumer products struggled to gain attention in an increasingly crowded space. One company, D.L. Blair, estimated it controlled some 80 percent of the corporate sweepstakes market (like the ones in children’s breakfast cereal) in 1979. However, it was the publishing industry that realized the full power of sweepstakes in driving sales, especially for magazine subscription. Reader’s Digest was one of the first to the party in 1962 having awarded nearly a million dollars a year until the end of the 1970s. The sweepstakes explosion in the 1960s and 70s led to a unique situation where magazine publishers were often paying out more to non-subscribers or the “no purchase necessary to enter” crowd than to those who subscribed. By 1979, Publishers Clearing House (PCH) had distributed over $7 million to some 2.3 million winners, most of whom weren’t driving revenue to the company. o § Science⠀➾ # ⚓ How_Do_Capacitors_Work?_|_Hackaday⠀⇛ If you are like [The Science Asylum], you might wonder how a capacitor can work since, at their core, they are nothing more than a gap filled with air or another insulator. He explains how in a recent video you can see below. Of course, at DC, a capacitor doesn’t conduct any better than the insulator used as its dielectric. However, a DC voltage has to start sometime and when it does, it briefly looks like AC. The video explains it all in simple terms. Of course, if you are math savvy, you can probably get as much out of the normal C=dQ/dV equation. If that doesn’t speak to you, the explanation in the video about charges will shed some light. He even shows an animation of the classic “hydraulic model”, which is helpful to develop intuition about the process. o § Hardware⠀➾ # ⚓ How_Many_Wires_Do_You_Need_To_Measure_A_Resistor?_| Hackaday⠀⇛ Measuring resistance doesn’t seem to be a big deal. Put your meter leads across two wires or terminals and read the value, right? Most of the time that is good enough, but sometimes you need better methods and for those, you need more wires, as [FesZ] explains in his recent video that you can see below. In the usual case, the meter applies a known voltage and measures the current which, by Ohm’s law, gives you the resistance. It is also possible to control the current and measure the voltage — doesn’t matter. [FesZ] shows how many meters measure voltage across a known resistor and the unknown so that a precision voltage or current source isn’t necessary. # ⚓ Tiger_Boy_Advance_Is_A_90s_Kid_Dream_Come_True_|_Hackaday⠀⇛ From the release of the DMG-01 in 1989 until the final Micro variant hit store shelves in 2005, the Nintendo Game Boy line represented the epitome of handheld gaming for hundreds of millions of players. But that’s not to say there weren’t a wide array of other handheld systems that aimed to chip away at the Japanese gaming giant’s monopoly. SEGA and Sony released high-tech systems that brought impressive technical innovations, while Tiger Electronics famously took the opposite approach with ultra-cheap handhelds that leveraged simplistic games based on popular children’s franchises. [Chris Downing] had to make do with these budget Tiger games as a child, and now as an adult, he’s determined to made things right with the Tiger Boy Advance. As the name implies, this retro hybrid combines the look and feel of a branded Tiger game with the power and software compatibility of a legitimate Nintendo Game Boy Advance (GBA) circa 2001. It even sprinkles in some modern niceties, like USB-C charging and a backlit display. While most of its charm is probably lost on anyone who didn’t grow up within a fairly narrow range of years, the video below seems to prove that even modern kids can appreciate this one-of-a-kind creation. # ⚓ A_Savage_Discussion_Of_Measurement_And_Accuracy_| Hackaday⠀⇛ Then, out come the Big Guns. The ceramic blocks so flat that… well you’ll just have to watch it. But the discussion goes deep into nanometers, microns, and jeweled movements. o § Health/Nutrition/Agriculture⠀➾ # ⚓ Today_in_America:_Moderna_CEO_tells_investment_bank_that COVID_won’t_end_and_vaccines_will_be_an_annual_product. Bonus:_Food_prices_off_the_charts._Don’t_turn_the_heater_on. –_BaronHK’s_Rants⠀⇛ Moderna’s CEO tells Goldman Sachs (mega investment bank) that COVID will never end, and vaccines will be an annual product now. “[Stephane] Bancel, while speaking at a health care event organized by Goldman Sachs, said that the booster efficacy will wane over time, similar to the first two shots of the COVID-19 vaccine.” Bancel added that COVID is “not going away.” o § Integrity/Availability⠀➾ # § Proprietary⠀➾ # § Security⠀➾ # ⚓ Reproducible_Builds_(diffoscope):_diffoscope 199_released⠀⇛ The diffoscope maintainers are pleased to announce the release of diffoscope version 199. This version includes the following changes: [ Chris Lamb ] * Support both variants of “odt2txt”, including the one provided by unoconv. (Closes: reproducible-builds/ diffoscope#298) [ Jelle van der Waa ] * Add external tool reference on Arch Linux for xb-tool. # ⚓ WordPress_Releases_Security_Update⠀⇛ WordPress versions between 3.7 and 5.8 are affected by multiple vulnerabilities. Exploitation of some of these vulnerabilities could cause a denial of service condition. # § Privacy/Surveillance⠀➾ # ⚓ Windows_10_is_a_data_privacy_nightmare⠀⇛ all those surveillance and “in app trying to sell something” make it way slower than Win 7… which is not good for a company that want’s to be productive (security, reliability, speed, speed, speed) o § Monopolies⠀➾ # § Patents⠀➾ # ⚓ FOSS_Patents:_Texas-based_Estech_Systems_targets_car makers_Toyota_and_BMW_in_rapidly_expanding_VoIP_patent assertion_campaign⠀⇛ There’s a gut instinct when a patent holder based in the Lone Star State files patent infringement lawsuits in the Eastern District of Texas against famous companies: “Oh, another non-practicing entity.” (or “troll” as some would call it) While Cisco dislikes certain patent enforcement tactics employed by Estech Systems (“ESI”), Estech is not a “patent troll.” According to its website, the company was founded in 1987 and “has sold over 400,000 phone systems and deployed more than three million phones nationwide.” ESI claims to have been “the first company to build a truly combined telephone and voice mail system, as well as the first to build a purely IP-based business communications system, and has numerous patents granted or pending on its products’ unique designs and capabilities.” # § Copyrights⠀➾ # ⚓ It’s_about_time_to_give_the_music_producer_her/his copyright_due_–_The_IPKat⠀⇛ Every songwriting process is a different story. You can get a closer look at it by watching ‘Diary of a song’ by The New York Times on YouTube, and documentaries such as Ed Sheeran’s ‘Songwriter’, or Shawn Mendes ‘In Wonder’. But all these stories have something in common. Nowadays, the song is usually composed using samples and artificial instruments. [...] Currently, a case may reach the Polish Supreme Court (a cassation appeal has been filed, but the Supreme Court has not yet decided whether to accept the case), in which the author of the entire arrangement of the song was not recognized as the co-author by the Court of Appeal. The judge ruled that the music producer created only a derivative work because lyrics and vocal melody could constitute a separate work. In this author’s view, if the music producer participates in the composing process, even if the work has several versions in the meantime, he should be considered as a co- author. However, if a music producer engages in a separate, independent process of creation, he/she should be recognized as an author of the derivative work. The clearest manifestation of the unity of the creative process is the cooperation in creating the final version of the work, based on mutual exchange of comments, guidelines, acceptance of stages of the creative process and versions of the work. ╘══════════════════════════════════════════════════════════════════════════════╛ ¶ Lines in total: 8054 ➮ Generation completed at 02:42, i.e. 89 seconds to (re)generate ⟲